'£ij^\'nmm:i':<'dif:i' 


UC-NRLF 


ii^i&SSIiifi^>.  m 


I  $B    E7fl    TM3 


•.SiJidJlHBirftMiliMd'.li'W 


Ele^e^taj^y 

\TMA\EriC 


R? 


» 


:i''  ? 


'i-\- 


W  MEMOEEAM 
Irving  Stringham 


Digitized  by  tine  Internet  Arciiive 

in  2007  witii  funding  from 

IVIicrosoft  Corporation 


littp://www.archive.org/details/elementaryaritlimOOwentricli 


A^ 


ELEMEN^TARY   ARITHMETIC, 


BY 
G.   A.   WENTVVORTH,   A.M., 

Author  of  a  Series  of  Text-Books  in  Mathematics. 


>o>«:;oc. — 


BOSTON,   U.S.A.: 

PUBLISHED  BY   GINN   &   CO. 

1894. 


Entered,  according  to  Act  of  Congress,  in  the  year  1893,  by 

G.   A.   WENTWORTH, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


All  Rights  Reserved, 


Typography  by  J.  S.  Gushing  &  Co.,  Boston,  U.S.A. 
Presswork  by  Ginn  &  Co.,  Boston,  U.S.A. 


'^^C^ 


PREFACE. 


Teachers  who  have  the  power  of  putting  themselves  in 
the  mental  attitude  of  their  pupils  possess  a  most  impor- 
tant gift.  In  the  first  stages  of  mental  growth,  as  the  mind 
works  unseen,  it  is  hard  to  realize  the  difficulties  encoun- 
tered, and  to  decide  what  assistance  can  be  judiciously 
given.  There  is  no  royal  road  to  the  knowledge  of  arith- 
metic, but  the  steps  can  be  made  short  and  easy.  The  little 
learner  need  not  be  wearied,  if  the  exercise  is  not  too  long 
continued.  He  may  also  have  the  consciousness  of  eifort, 
as  in  learning  to  walk,  and  above  all,  the  pleasure  of  suc- 
ceeding. This  result  can  be  secured  only  by  observing  the 
following  fundamental  principles  : 

1.  All  elementary  teaching  of  arithmetic  must  be  begun  by 
the  pupils  observing  and  handling  objects. 

It  is  surprising  that  school  authorities  in  many  places 
decline  to  furnish  the  money,  however  small  the  amount  is, 
to  purchase  the  simple  apparatus  required  for  each  Primary 
School.  They  assert  that  they  got  on  well  enough  without 
such  aids  when  they  were  children,  and  they  seem  to  be 
quite  unconscious  of  the  weakness  of  such  an  argument. 
The  question  is  not  whether  children  can  do  well  without 
the  aid  of  objects,  but  whether  they  can  do  better  with 
them.  Our  fathers  did  well  enough  in  travelling  on  horse- 
back and  in  coaches,  but  we  do  better  with  our  express 
trains.  Children  may  be  able  to  grasp  abstract  ideas,  after 
sufficient  time,  without  the  aid  of  concrete  examples.     It 

8005&? 


iv  PREFACE. 

is  certain,  however,  that  they  grasp  these  ideas  more  firmly 
and  more  quickly  if  they  are  led  to  them  by  easy  steps 
through  objects  that  can  be  seen  and  handled. 

Besides,  the  use  of  objects  saves  children  from  the 
bondage  of  rules.  With  6  blocks  they  can  learn  to  add 
4  and  2,  to  subtract  4  from  6,  to  multiply  3  by  2,  to  divide 
6  by  2,  without  suspecting  the  existence  of  the  fearful  rules 
to  be  found  in  our  text-books  of  arithmetic.  They  can  also 
be  taught  to  find  ^  of  6  or  |  of  6,  without  even  hearing 
of  the  terms,  fraction,  numerator,  or  denominator. 

2.  A  knowledge  of  the  processes  of  arithmetic  should  be 
acquired  by  using  small  numbers  ;  and  each  number  should  be 
treated  in  all  its  variations  before  the  next  higher  number  is 
considered. 

In  the  treatment  of  each  number  we  must  rely  upon  the 
sight  of  the  pupil,  and  not  upon  his  hearing.  Furthermore, 
we  must  rely  upon  his  activity.  He  must  do  as  well  as 
see.  Listless  repetition  of  4  and  3  are  7,  or  the  sing-song 
4  times  3  are  12,  makes  no  impression  upon  him.  The  next 
day  he  is  quite  likely  to  tell  you  that  4  and  3  are  6.  If  he 
is  required  to  put  4  pegs  in  one  row  of  the  counting-board 
and  3  in  another  row,  and  to  learn  in  this  way  that  4  and  3 
are  7,  he  will  remember  it.  This  method  of  teaching  has 
the  very  great  advantage  of  keepmg  the  child's  interest  in 
his  work  fully  alive,  and  of  giving  to  the  study  of  arith- 
metic the  peculiar  distinction  that  the  learner  can  discover 
for  himself,  in  case  of  doubt,  whether  his  answer  to  any 
question  is  right  or  wrong,  and  can  find  the  true  answer, 
if  he  has  given  a  wrong  one. 

3.  Repetition  is  to  be  regular  and  systematic,  combined 
with  suitable  variation. 

It  cannot  be  too  strongly  urged  that  the  first  requisite  of 
good  teaching  is  repetition,  the  second  requisite  is  repeti- 
tion, and  the  third  requisite  is  repetition.     The  interest  of 


PREFACE.  V 

the  pupil  must  be  kept  up  by  varying  the  application  of  the 
question.  To  find  the  sum  of  3  horses  and  5  horses  is  not 
the  same  thing  to  the  child  as  to  find  the  sum  of  3  tops  and 
5  tops.  Hence  a  lesson  may  be  ^iven  as  many  times  as 
may  be  necessary  by  properly  varying  the  questions. 

A  table  of  different  things,  given  opposite  the  first  page 
of  this  book,  will  be  found  of  great  use  in  suggesting  a 
suitable  variety  of  questions.  Care  must  be  exercised  to 
have  the  variation  of  a  kind  to  fix  knowledge.  To  ask  the 
number  of  3  ducks  and  4  ducks,  of  3  times  4  ducks,  and 
\  of  12  ducks,  in  succession,  is  a  variation,  to  be  sure,  but  of 
a  kind  to  distract  the  child's  mind,  as  he  cannot  quickly 
pass  from  one  conception  to  the  other.  The  questions  in 
Part  I.  of  this  book  are  specimen  questions,  which  it  is 
expected  the  Teacher  will  supplement  by  a  great  number 
and  variety  of  other  questions. 

4.  Lessons  should  be  short,  answers  required  should  be 
simple,  and  the  power  to  deal  with  numbers  in  the  abstract 
should  be  acquired  through  concrete  examples  by  regular 
gradation. 

Number  work  should  be  discontinued  the  moment  the 
pupil's  attention  flags.  It  is  far  better  to  divide  the  time 
daily  allotted  to  arithmetic  into  two  or  more  lessons.  Only 
simple,  direct  answers  should  be  required.  Of  course,  if 
objects  are  named  in  the  question,  they  should  be  named  in 
the  answer.  The  answer  to  5  birds  +  3  birds  should  be 
8  birds,  and  not  simply  8. 

A  knowledge  of  numbers  in  the  abstract  is  obtained  only 
by  a  comparison  of  different  things.  The  child  learns  the 
number  5,  for  instance,  by  seeing  and  handling  5  familiar 
objects,  by  observing  number  pictures  of  5  on  the  black- 
board or  on  cardboard,  by  answering  questions  about  5 
familiar  but  unseen  objects,  and  lastly  about  5  in  the 
abstract. 


Vi  PREFACE. 

5.  The  child  must  not  be  required  to  read  questions  that  are 
difficult  for  him  to  read,  or  to  solve  problems  that  are  difficult 
for  him  to  analyze. 

The  intention  is  to  put  this  book  into  the  hands  of  young 
pupils,  hut  only  for  them,  to  copy  and  do  the  nmnerical  exer- 
cises. The  other  examples,  usually  called  clothed  examples 
by  way  of  distinction,  must  be  read  by  the  Teacher,  and  only 
the  answers  be  required  of  pupils.  No  child  can  become 
interested  or  successful  in  arithmetic  if  his  mind  is  dis- 
tracted between  the  reading  of  a  problem  and  the  numerical 
calculation  required  for  its  solution.  He  can  learn  the 
simple  processes  of  arithmetic  while  quite  young ;  he  can 
learn  to  be  accurate  and  reasonably  rapid  in  these  processes ; 
he  can  learn  to  be  neat  and  orderly  in  the  arrangement  of 
his  work ;  and  his  interest  will  constantly  increase,  pro- 
vided he  is  kejyt  master  of  his  field  of  operations.  At  this 
early  stage  he  cannot  be  exercised  in  logical  analysis,  and  it 
is  a  great  mistake  to  put  problems  before  him  that  require 
too  great  an  exercise  of  the  reasoning  faculty.  Later  he 
will  form  the  habit  of  close  attention,  learn  the  meaning  of 
logical  inference,  and  acquire  the  power  of  sustained  and 
continuous  thought.  Arithmetic  rightly  taught  furnishes 
the  very  essence  of  intellectual  training,  and  deserves  the 
name  of  "The  Logic  of  the  People." 

G.    A.   WENTWORTH. 

EXKTEK,    N.H. 


TABLE   FOR   VARYING   QUESTIONS. 


Animals.  .  .  .  Dog,  Puppy,  Cat.  Kitten,  Rabbit,  Cow,  Calf,  Pig,  Horse, 
Colt,  Sheep.  Lamb,  Goat,  Kid,  Fox,  Mouse,  Squirrel, 
Monkey. 

Birds o  Robin,  Sparrow,  Swallow,  Canary,  Parrot,  Crow,  Blue- 
bird, Kingbird,  Hawk,  Owl,  Jay,  Loon,  Swan,  Pigeon. 

Clothes  ....  Hat,  Cap,  Bonnet,  Coat,  Vest,  Dress,  Socks,  Boots,  Shoes, 
Collar,  Cuffs,  Slippers,  Rubbers,  Mittens,  Gloves. 

Flowers  ....  Rose,  Pink,  Daisy,  Pansy,  Lily,  Geranium,  Violet,  Poppy. 

Fowls Hen,  Chicken,  Turkey,  Duck,  Goose,  Gosling. 

Fruits Apple,  Pear,  Quince,  Orange,  Lemon,  Peach,  Grape,  Fig. 

Garden Peas,  Beans,  Corn,  Potatoes,  Carrots,  Parsnips. 

House Room,  Door,  Window,  Chair,  Table,  Picture,  Carpet,  Cup, 

Plate,  Saucer,  Fork,  Knife,  Spoon,  Pitcher,  Clock. 

Insects Fly,  Spider,  Bee,  Hornet,  Butterfly,  Beetle,  Cricket. 

School Desk,  Slate,  Pencil,  Pen,  Book,  Paper,  Chair. 

Smallwares. .  Buttons,  Pins,  Needles,  Spools  of  Thread. 

Store Tea,    Coffee,   Sugar,    Starch,    Soap,    Candles,    Matches, 

Eggs,  Axe,  Rake,  Pail,  Spade,  Hoe,  Saw,  Nails. 

Toy-Store.  .  .  Doll,  Top,  Ball,  Whip,  Basket,  Marbles,  Whistle. 

Tradesmen.  .  Baker,  Butcher,  Grocer,  Milkman,  Blacksmith. 

Trees Apple,  Oak,  Cherry,  Plum,  Ash,  Birch,  Beech. 

Vehicles  .  .  .  Train,  Car,  Coach,  Hack,  Buggy,  Wagon,  Gig,  Sleigh, 
Sled,  Barge,  Bus. 


•  •     t  J  • 


Elementary  Arithmetic. 


Part  I. 


Part  T.  is  intended  as  a  guide  to  teachers  in  oral  and  blackboard 
work  for  children  before  they  can  read.  After  they  can  read,  a  rapid 
review  will  help  fix  their  knowledge  of  simple  arithmetical  processes. 

THINGS    NEEDED. 

1.  Objects  for  Counters.  Such  as  cents,  blocks,  buttons,  spools, 
pencils,  nails,  little  tin  plates,  cups  and  saucers,  inch-squares  of  paste- 
board, foot-rules,  yard-sticks,  a  set  of  tin  measures  for  liquids,  a 
set  of  wooden  measures  for  dry  articles,  and  a  set  of  weights. 

2.  A  Counting-Board.  This  is  of  great  assistance  in  teaching  arith- 
metical processes  with  small  numbers.  It  is  simply  a  smooth  board 
with  100  holes  about  an  inch  apart,  arranged  in  10  rows  of  10  holes 
each.     Nails  or  wooden  pins  can  be  used  for  counters. 

Another  way  of  making  the  counting-board  is  to  drive  100  nails 
ill  10  rows  of  10  nails  each  through  a  piece  of  board,  at  suitable  dis- 
tances from  each  other,  until  they  project  about  an  inch,  and  use 
spools  for  counters,  slipping  them  on  the  ends  of  the  nails. 


LESSON   1. 
THE  NUMBER  ONE. 

Show  me  one  finger  ;  one  block  ;  one  button. 
How  many  suns  do  we  see  by  day  ?    How  many 
moons  by  night  ? 

We  write  the  figure  1  for  one. 

Note.  The  introduction  of  tigures  may  be  postponed  until  after  the 
number  six  is  taught.  In  that  case  some  variation  in  the  language 
will  be  required. 

1 


2  LESSON   2. 

THE    NUMBER    TWO. 

How  many  fingers  are  one  finger  and  one  finger  ? 
Hold  up  two  fingers  ;  two  hands. 
We  write  the  figure  2  for  two. 

NoTK,    Pictures  of  balls,  cups,  tops,  blocks,  etc.,  are  introduced  in 
places  where  it  is  expected  the  Teacher  will  show  objects  of  some  kind. 

How  many  balls  are  C)  and  C)  ? 

How  many  cups  are  "Q  and  Q*  ? 

How  many  dolls  are  1  doll  and  1  doll  \ 

How  many  horses  are  1  horse  and  1  horse  ? 

How  many  are  1  and  1  ? 

Here  are  two  blocks,  B  8-  Take  away  jB. 
How  many  are  left  ? 

1  apple  from  2  apples  leaves  how  many  ? 

1  from  2  leaves  how  many  ? 

How  many  more  pears  are  ^  ^  than  ^  ? 

How  many  more  dolls  are  2  dolls  than  1  doll  ? 

How  many  rings  must  you  put  with  O  to 
have  O    O  • 

How  many  apples  must  you  put  with  1  apple  to 
have  2  apples  ? 

Note.  The  following  plan  is  recommended  to  the  Teacher,  for  the 
number-work  of  Part  I. : 

1.  Show  objects,  and  secure  the  desired  result  from  them. 

2.  Draw  pictures  of  blocks,  squares,  etc.,  on  the  board,  and  obtain 
the  same  result  from  the  pictures. 

3.  Ask  the  same  question  on  familiar  but  unseen  objects. 

4.  Finish  with  abstract  numbers. 

The  Teacher  can  vary  the  questions  at  pleasure  by  using  different 
objects  and  different  pictures^  and  by  using  the  table  of  familiar  objects 
given  opposite  the  first  page. 


LESSON  3. 


3 


THE  NUMBER  THREE. 

How  many  fingers  are  tivo  fingers  and  one  finger  ? 

Hold  up  three  fingers. 

We  write  the  figure  3  for  three. 

*  Copy  each  card  below,  and  write  under  it  the 
figure  for  the  number  of  dots  in  the  card  : 


•  •  •  •*• 


Count  the  dots  in  these  cards  from  left  to  right. 
Count  the  dots  from  right  to  left. 
What  number  follows  1  ?  What  number  follows  2  ? 
What  number  comes  before  2  ?  before  3  ? 
What  number  is  between  1  and  3  ? 
*  Copy  these   pictures,  and   write   under   each 
group  the  figure  for  the  number  in  the  group. 

AAA  DDD  ••• 

XXX  OOO  *** 

How  many  pears  are  ^  and  ^  and  ^  ? 

How  many  balls  are  ®  and  ©  and  ©  ? 

How  many  dogs  are  1  dog  and  1  dog  and  1  dog  ? 

How  many  boys  are  1  boy  and  1  boy  and  1  boy  ? 

How  many  are  1  and  1  and  1  ? 

How  many  stars  are  >|<  if  and  >)<  ? 

*NoTE.  In  this  case  and  in  similar  cases  tlie  Teacher  should  put  the 
number  pictures  on  the  board,  and  then  require  the  pupils  to  follow 
the  directions  given.  The  Teacher  should  require  the  attention  of  the 
pupils  only  a  few  minutes  at  a  time.  One  of  these  "Lessons"  will 
make  a  great  many  lessons  for  the  children. 


4  LESSON  4. 

How  many  apples  are  C5  ^^^  ^  C3  ^ 
How  many  pinks  are  1  pink  and  2  pinks  ? 
How  many  are  1  and  2  ?  2  and  1  ? 

Here  are  three  blocks,  11  B  HP 
Take  1  block  away,  how  many  will  be  left  ? 
Take  2  blocks  away,  how  many  will  be  left  ? 
Take  3  blocks  away,  how  many  will  be  left  ? 
How  many  more  blocks  are  11811  than  8  B  ? 
How  many  more  cows  are  3  cows  than  2  cows  ? 
How  many  more  figs  are  3  figs  than  1  fig  ? 

How  many  blocks  must  be  put  with  ||  to  make 

S  IB  S  ^ 

How  many  baskets  must  be  put  with  ^^  ^^ 
to  make  ^^    ^^  ^^  ? 

How  many  plums  must  be  put  with  2  plums  to 
make  3  plums  ? 

How  many  plums  must  be  put  with  1  plum  to 
make  3  plums  ? 

James  may  take  1  block ;  then  1  more ;  and 
then  1  more. 

How  many  times  has  James  taken  1  block  ?  How 
many  blocks  has  he  ?  Then  3  times  1  block  are 
how  many  blocks  ? 

How  many  chairs  are  3  times  1  chair  ? 

Here  are  3  apples,  C^  C5  ®-  How  many  boys 
can  each  have  1  apple  ? 

Here  are  3  dolls.  How  many  girls  can  each 
have  1  doll  ?     How  many  07ies  in  3  ? 


LESSON   5.  6 

THE  NUMBER  FOUR. 

Three  dots  and  one  dot  make  four  dots. 
Here  arefoitr'  dots,  •  •  •  • 
We  write  the  figure  4  for  four. 

Copy  each  card  below,  and  write  under  it  the 
figure  for  the  number  of  dots  in  the  card : 


•  •  • 

•  •  • 

•  •  •  • 


Count  the  dots  in  these  cards  from  left  to  right. 
Count  the  dots  from  right  to  left. 
What  number  follows  2  ?  What  number  follows  3  ? 
What  number  comes  before  4  ?   before  3  ? 
What  number  is  between  1  and  3  ?    2  and  4  ? 

Copy  these  pictures,  and  write  under  each  group 
the  figure  for  the  number  in  the  group  : 

****  oooo 

How  many  sides  has  this  square  Q  ? 
How  many  legs  has  a  horse  ?   a  frog  ?   a  cow  ? 
How  many  stars  are  >)c  >)c  >)<  and  >(<  ? 
How  many  rings  are   O  O  O  ^^^id  Q  ? 
How  many  crosses  are  +  and  +  +  +  '^ 
Ho\^  many  eggs  are  o  and  o  o  O  ? 
How  many  boys  are  3  boys  and  1  boy  ? 
How  many  mice  are  1  mouse  and  3  mice  ? 
How  many  are  3  and  1  ?    1  and  3  ? 


6  LESSON   6. 

How  many  stars  are  >|c  >|<  and  >|c  >|<  ? 

How  many  marks  are  //  and  //  ? 

How  many  brooms  are  2  brooms  and  2  brooms  ? 

How  many  are  2  and  2  ? 

Here  are  four  blocks,  11111111 

Cover  one  block.     How  many  can  you  see  ? 

Then  1  from  4  leaves  how  many  ? 

Cover  two  blocks.     How  many  can  you  see  ? 

Then  2  from  4  leaves  how  many  ? 

Cover  three  blocks.     How  many  can  you  see  ? 

Then  3  from  4  leaves  how  many  ? 

Cover  all  four  blocks.     How  many  can  you  see  ? 

Then  4  from  4  leaves  how  many  ? 

How  many  more  tops  are  <<iJP  'iijp  "iijp  ^  than  ^  <%)  ^  ? 

How  many  more  balls  are  ©®  ©©  than  ©©? 

How  many  more  crosses  are  ►f*  ►I^  ►!<  ►{<  than  ►ff  ? 
*  How  many  more  cars  are  4  cars  than  3  cars  ? 
than  2  cars  ?    than  1  car  ? 

How  many  more  apples  are  4  apples  than  2 
apples  ?   than  1  apple  ?   than  3  apples  ? 

How  many  ladders  must  be  put  with  0  to  make 

How  many  pears  must  be  put  with  (^  ^  to 

make  d  d  d  d  ? 

How  many  crosses  must  be  put  with  X  X  X  to 

make  XX  XX? 

*  The  Teacher  must  make  the  question  complete  in  each  case. 
Thus,  How  many  more  cars  are  4  cars  than  3  cars  ?  How  many  more 
cars  are  4  cars  than  2  cars  ?   How  many  more  cars  are  4  cars  than  1  car  ? 


LESSON   7.  7 

Here  are  4  blocks,  f|  H  0  ii 

Susie  may  take  1  block ;  then  1  more ;  then  1 
more ;  and  then  1  more.  How  many  times  has 
Susie  taken  1  block  ?  How  many  blocks  has  she  ? 
Then  how  many  blocks  are  4  times  1  block  ? 

How  many  apples  are  4  times  1  apple  ? 

How  many  figs  are  4  times  1  fig  ? 

How  many  are  4  times  1  ? 

Ernest  may  take  2  blocks;  and  then  2  more. 
How  many  times  has  Ernest  taken  2  blocks  ?  How 
many  blocks  has  he  ?  Then  how  many  blocks  are 
2  times  2  blocks  ? 

How  many  cakes  are  2  times  2  cakes  ? 

How  many  rolls  are  2  times  2  rolls? 

How  many  are  2  times  2  ? 

Here  are  4  apples,  C5  (3  (3  C5.  How  many 
boys  can  have  1  apple  each  ?    How  many  ones  in  4  ? 

Here  are  4  tops,  (yf)  ^  <(i{;)  <<$).  How  many  boys 
can  have  2  tops  each  ?     How  many  twos  in  4  ? 

Here  are  4  dots,  •  •  •  • 

Divide  them  into  tioo  equal  parts,  thus  •  •/•  • 
How  many  dots  in  each  part  ? 
When  a  number  of  things  is  divided  into  two 
equal  parts,  each  part  is  called  one-half  of  the  whole 
number. 

What  is  one-half  of 

4  blocks  ?        4  pears  ?         4  cents  ? 
4  books  ?         4  buns  ?  2  oranges  ? 


LESSON  8. 
THE  HALF  OF  A  UNIT. 


If  an  apple  is  cut  into  two  equal  parts,  what  is 
one  of  the  parts  called  ? 

What  are  the  two  parts  called  ? 

If  an  orange  is  divided  into  two  equal  parts, 
what  is  one  of  the  parts  called  ? 

If  anything  is  divided  into  two  equal  parts, 
what  is  one  of  the  parts  called  ? 

How  many  halves  of  an  apple  in  a  whole  apple  ? 

How  many  halves  of  an  orange  make  the  whole 
orange  ? 

How  many  halves  of  anything  make  the  whole 
thing  ? 

How  many  times  must  you  take  one-half  of  an 
apple  to  have  an  apple  ? 

If  one-half  of  an  orange  is  worth  2  cents,  how 
many  cents  is  the  orange  worth  ? 

If  an  apple  is  worth  2  cents,  how  much  is  one- 
half  of  the  apple  worth  ? 

How  many  halves  of  an  apple  in  two  whole 
apples  ? 

How  many  halves  of  an  apple  in  one  whole 
apple  and  one-half  of  another  apple  ? 

Draw  a  straight  line  and  divide  it  into  halves. 

Draw  a  square  and  divide  it  into  halves. 


LESSON   9.  9 

THE  NUMBER  FIVE. 

Four  dots  and  one  dot  make  five  dots. 

Here  are  five  dots,  J«J 

We  write  the  figure  5  for  five. 

How  many  fingers  on  your  right  hand  ? 
How  many  fingers  on  your  left  hand  ? 
Copy  these  pictures,  and  write  under  each  group 
the  figure  for  the  number  in  the  group : 

AAAAA  XXXXX 

+++++  o  o  o  o  o 

Copy  each  card  below,  and  write  under  it  the 
figure  for  the  immber  of  dots  in  the  card  : 


•  •    •  .  *  ^  • 


Count  the  dots  in  these  cards  from  left  to  right. 
Count  the  dots  from  right  to  left. 
What  number  follows  4  ?  What  number  follows  2  ? 
What  number  comes  before  5  ?  before  2  ?  before  4? 
What  number  is  between  3  and  5  ?   2  and  4  ? 
How  many  stars  are  >)<  >|<  >|<  >(c  and  >)<  ? 
How  many  tops  are  <iif)  'iiJP  "iif  <(ij)  and  ^  ? 
How  many  ladders  are  ^  and  ^  ^  ^  ^  ? 
How  many  crosses  are  +  and  +  H — I — h  ? 
How  many  apples  are  4  apples  and  1  apple  ? 
How  many  plums  are  1  plum  and  4  plums  ? 
How  many  are  4  and  1  ?    1  and  4  ? 


10  LESSON   10. 

How  many  marks  are  /  /  and  /  /  /  t 

How  many  bottles  are    Q    fl  and  (^    (^   (^  ? 

How  many  balls  are  <©  ©  ©  ^^^  ©  ®  ? 

How  many  mugs  are  ^Q  '^  ^  and  ^^  ^  ? 

How  many  figs  are  3  figs  and  2  figs  ? 

How  many  spoons  are  2  spoons  and  3  spoons  ? 

How  many  cars  are  3  cars  and  2  cars  ? 

How  many  lambs  are  3  lambs  and  2  lambs  ? 

How  many  are  2  and  3  ? 

How  many  are  3  and  2  ? 

Here  are  five  blocks,  11  B  ||  B  B 

Cover  one  block.     How  many  can  you  see  ? 

Then  1  from  5  leaves  how  many  ? 

Cover  two  blocks.     How  many  can  you  see  ? 

Then  2  from  5  leaves  how  many  ? 

Cover  three  blocks.     How  many  can  you  see  ? 

Then  3  from  5  leaves  how  many  ? 

Cover  four  blocks.     How  many  can  you  see  ? 

Then  4  from  5  leaves  how  many  ? 

Cover  five  blocks.     How  many  can  you  see  ? 

Then  5  from  5  leaves  how  many  ? 

How  many  more  dots  are  •  •  •  •  •  than  •  •  •  •  ? 

How  many  more  stars  are  *****  than  *  *  *  ? 

How  many  more  crosses  are  x  x  x  x  x  than  x  x  ? 

How  many  more  balls  are  ©  ©  ©  ©  ©  than  ©  ? 

How  many  more  hens  are  5  hens  than  3  hens  ? 

How  many  more  dogs  are  5  dogs  than  2  dogs  ? 

How  many  more  lambs  are  5  lambs  than  4  lambs? 

How  many  more  pigs  are  5  pigs  than  1  pig  ? 


LESSON   11.  11 

How  many  rings  must  be  put  with  O  to  make 

O  O  O  O  O? 

How  many  stars  must  be  put  with  *  *  *  *  to 
make  ****>!<? 

How  many  crosses  must  be  put  with  x  x  to 
make  x  x  x  x  x  ? 

How  many  marks  must  be  put  with  ///  to  make 

/////? 

How  many  cents  must  be  put  with  2  cents  to 
make  5  cents  ? 

How  many  balls  must  be  put  with  3  balls  to 
make  5  balls  ? 

How  many  pigeons  must  be  put  with  1  pigeon 
to  make  5  pigeons  ? 

How  many  pears  must  be  put  with  4  pears  to 
make  5  pears  ? 

If  Frank  takes  1  block  at  a  time  for  5  times, 
how  many  blocks  will  he  have  ? 

Then  5  times  1  block  are  how  many  blocks  ? 

5  times  1  apple  are  how  many  apples  ? 

5  times  1  cup  are  how  many  cups  ? 

Here  are  5  tops,  <<I5?  ^  <iif>  "iiJP  <!$) 

How  many  boys  can  have  1  top  apiece  ? 
■  How  many  ones  in  5  ? 

How  many  boys  can  have  2  tops  apiece  ? 

How  many  will  be  left  for  another  boy  ? 

How  many  tivos  in  5,  and  how  many  over  ? 

How  many  threes  in  5,  and  how  many  over  ? 

How  many/o77r.s  in  5,  and  how  many  over? 


12 


LESSON   12. 


THE  NUMBER  SIX. 

Five  dots  and  one  dot  make  six  dots. 

Here  are  six  dots,  J  J  J 

We  write  the  figure  6  for  six. 

Copy  these  pictures,  and  write  under  eacli  group 
the  figure  for  the  number  in  the  group  : 

>f:   ***:+:   >^  ////// 

AAAAAA  xxxxxx 

oooooo     nnnnna 


o  o  o  o  o  o 


Copy  each  card  below,  and  write  under  it  tlie 
figure  for  the  number  of  dots  in  the  card  : 


•  •  • 

•  •  • 


Count  these  dots  from  left  to  right. 
Count  these  dots  from  right  to  left. 
What  number  follows  4  ?  What  number  follows  5  ? 
What  number  comes  before  4  ?    before  6  ?  be- 
fore 5  ?   before  3  ?   before  2  ? 

What  number  is  between  4  and  6  ?    3  and  5  ? 
How  many  balls  are  C)  ©  ©  ©  ©  and  ©  ? 
How  many  tops  are  ^  and  ^  <t9  ^  *¥^  "V^  ? 
How  many  boxes  are  5  boxes  and  1  box  ? 
How  many  brooms  are  1  broom  and  5  brooms  ? 
How  many  birds  are  5  birds  and  1  bird  ? 
How  many  oranges  are  1  orange  and  5  oranges  ? 
How  many  are  5  and  1  ?    1  and  5  ? 


LESSON   13.  13 

How  many  stars  are  >|c  >|<  >|c  >)<  and  >♦<  >|<  ? 

How  many  rings  are  O  O  and  O  O  O  O  '^ 

How  many  balls  are  ©  ©  and  <©  ©  aiid  ©  ©  ? 

How  many  kittens  are  4  kittens  and  2  kittens  ? 

How  many  horses  are  4  horses  and  2  horses  ? 

How  many  buns  are  2  buns  and  4  buns  ? 

How  many  pies  are  2  pies  and  4  pies  ? 

How  many  are  4  and  2  ?    2  and  4  ? 

How  many  crosses  are  ►!<  ►t"  ♦  and  ^  ^  «{^  ? 

How  many  apples  are  3  apples  and  3  apples  ? 

How  many  are  3  and  3  ? 

Here  are  6  blocks,  fp  fp  0  0  H  ip 

Cover  1  block.     How  many  can  you  see  ? 

Then  1  from  6  leaves  how  many  ? 

Cover  2  blocks.     How  many  can  you  see  ? 

Then  2  from  6  leaves  how  many  ? 

Cover  3  blocks.     How  many  can  you  see  ? 

Then  3  from  6  leaves  how  many  ? 

Cover  4  blocks.     How  many  can  you  see  ? 

Then  4  from  6  leaves  how  many  ? 

Cover  5  blocks.     How  many  can  you  see  ? 

Then  5  from  6  leaves  how  many  ? 

Cover  6  blocks.     How  many  can  you  see  ? 

Then  6  from  6  leaves  how  many  ? 

How  many  more  dots  are  ••••••  than  •••••? 

How  many  more  stars  are  ******  than  ****  ? 
How  many  more  crosses  are  x  x  x  x  x  x  than  x  x  x  ? 
How  many  more  marks  are  1 1 1 1 1 1  than  /  /  ? 
How  many  more  tops  are  ^^^^^<iif>  than  ^  ? 


14  LESSON   14. 

How  many  more  chairs  are  6  chairs  than  5  chairs? 

How  many  more  boxes  are  6  boxes  than  4  boxes  ? 

How  many  more  cars  are  6  cars  than  3  cars  ? 

How  many  more  dogs  are  6  dogs  than  2  dogs  ? 

How  many  more  pears  are  6  pears  than  1  pear  ? 

How  many  marks  must  be  put  with  1 1 1 1 1  to 
make//////? 

How  many  tops  must  be  put  with  <<i5>  <i9  *¥^  V'  to 
make  *ii|P  "tiip  ^  "ij^  "tip  <i^  ? 

How  many  stars  must  be  put  with  *  *  *  to 
make  *  *  *  -)f  *  *  ? 

How  many  balls  must  be  put  with  ©  ©  to  make 

©©€)©€)€)? 

How  many  squares  must  be  put  with  n  to  make 
D  D  D  D  D  D  ? 

How  many  bells  must  be  put  with  3  bells  to 
make  6  bells  ? 

How  many  caps  must  be  put  with  2  caps  to 
make  6  caps  ? 

How  many  pies  must  be  put  with  4  pies  to  make 
6  pies  ? 

How  many  cups  must  be  put  with  1  cup  to  make 
6  cups  ? 

How  many  books  must  be  put  with  5  books  to 
make  6  books  ? 

Here  are  6  blocks,  %%    B  B    B  B 

If  Hattie  takes  2  blocks  at  a  time  for  3  times, 
how  many  blocks  will  she  have  ? 

Then  how  many  blocks  are  3  times  2  blocks  ? 


LESSON   15.  15 

Here  are  6  blocks,  SMS    0  0  0 
John  may  take  3  blocks ;  then  3  more. 
How  many  times  has  John  taken  3  blocks? 
How  many  blocks  has  he  ? 
Then  how  many  blocks  are  2  times  3  blocks  ? 
How  many  oranges  are  2  times  3  oranges  ? 
How  many  are  2  times  o  ? 

Here  are  6  apples,  C5   (^    O    C3   O    C5 

How  many  girls  can  have  1  apple  each  ? 

How  many  07ies  in  6  ? 

How  many  girls  can  have  2  apples  each  ? 

How  many  tivos  in  6  ? 

How  many  girls  can  have  3  apples  each  ? 

How  many  threes  in  6  ? 

Here  are  6  dots,  •••••• 

Divide  them  into  two  equal  parts,  •  •  •/•  •  • 
How  many  dots  are  there  in  each  part  ? 
What  is  one-half  of  6  dots  ?   6  cents  ? 
What  is  one-half  of  4  apples  ?   2  pens  ? 
Divide    6    dots    into    three    equal    parts,    thus. 

How  many  dots  are  there  in  each  part  ? 
When  a  number  of  things  is  divided  into  three 
equal  parts,  each  part  is  one-third  of  the  number. 
What  is  one-third  of  6  dots  ?   of  6  cents  ? 
How  many  dots  are  two-thirds  of  6  dots  ? 
How  many  dots  are  three-thirds  of  6  dots  ? 
How  many  oranges  are  two-thirds  of  6  oranges  ? 


16  LESSON   16. 


Into  how  many  equal  parts  is  this  pineapple  cut  ? 

AVhat  is  one  of  the  parts  called  ? 

What  are  two  of  the  parts  called  ? 

What  are  the  three  parts  together  called  ? 

If  a  circle  is  cut  into  three  equal 
parts,  what  is  one  of  the  parts  called  ? 
two  of  the  parts  ?  the  three  parts  ? 

How  many  thirds  of  an  apple  in  one 
apple  ? 

How  many  thirds  of  an  apple  in  two  apples  ? 

How  many  thirds  of  an  apple  in  one  apple  and 
one-third  of  an  apple  ? 

How  many  thirds  of  an  apple  in  one  apple  and 
two-thirds  of  an  apple  ? 

If  an  orange  is  worth  3  cents,  how  many  cents 
is  one-third  of  the  orange  worth  ? 

If  one-third  of  a  big  stick  of  candy  is  worth 
2  cents,  how  many  cents  is  the  whole  stick  worth  ? 

John  had  a  stick  of  candy,  but  he  gave  his  little 
sister  one-third  of  it.  How  many  thirds  of  the 
stick  had  he  left  ? 

James  had  to  walk  from  his  house  to  the  school- 
house.  After  he  had  walked  two-thirds  of  the 
way,  how  many  more  thirds  had  he  to  walk  ? 


LESSON   17.  17 

How  many  apples  at  2  cents  apiece  can  you  buy 
for  4  cents  ? 

NoTK.    The  answer  required  should  be  simply  :  2  apples. 

How  many  boots  does  it  take  to  make  a  pair  of 
boots  ?    How  many  horses  to  make  a  pair  of  horses  ? 

How  many  pairs  of  boots  does  it  take  for  3  boys  ? 

How  many  boots  in  2  pairs  of  boots?  How 
many  horses  in  3  pairs  of  horses  ?  How  many 
oxen  in  3  pairs  of  oxen  ? 

The  butcher  has  2  horses,  the  grocer  2  horses, 
and  the  baker  has  1  horse.  How  many  horses 
have  they  in  all  ? 

Mary  has  3  cages,  and  1  bird  in  each  cage.  How 
many  birds  has  she  ? 

There  were  5  sheep  in  the  pasture,  and  each 
sheep  had  1  lamb.     How  many  lambs  were  there  ? 

There  were  5  apples  on  a  limb.  Three  fell  off. 
How  many  were  left  ? 

Harold  had  5  cents,  and  bought  a  ball  for  2 
cents.     How  many  cents  did  he  have  then  ? 

A  blacksmith  had  6  horses  to  shoe.  He  shod 
half  of  them.     How  many  more  had  he  to  shoe  ? 

A  blacksmith  shod  4  horses  before  dinner,  and 
2  after  dinner.     How  many  did  he  shoe  ? 

John  and  his  papa  hoed  6  rows  of  corn.  John 
hoed  one-third  of  the  6  rows,  and  his  papa  two- 
thirds  of  them.     How  many  rows  did  each  hoe  ? 

What  part  of  6  apples  are  2  apples  ? 

What  part  of  6  apples  are  3  apples  ? 


18  LESSON   18. 

At  3  cents  apiece  how  many  oranges  can  you  buy 
for  6  cents  ? 

At  2  cents  apiece  how  many  apples  can  you  buy 
for  6  cents  ? 

If  you  can  buy  3  sticks  of  candy  for  3  cents, 
how  many  sticks  can  you  buy  for  4  cents  ? 

If  you  have  6  eggs,  2  on  a  plate,  how  many 
plates  have  you  ? 

If  you  can  buy  2  apples  for  2  cents,  how  many 
apples  can  you  buy  for  6  cents  ? 

What  is  one-half  of  6  cents  ?  one-third  of  6  cents  ? 
two-thirds  of  6  cents  ?   three-thirds  of  6  cents  ? 

Charlie  sold  3  newspapers  for  2  cents  a  paper. 
How  many  cents  did  he  get  for  the  3  papers  ? 

It  takes  2  cents  to  buy  a  paper.  Hoav  many 
papers  can  you  buy  for  4  cents  ?   for  6  cents  ? 

If  you  have  six  cents,  and  spend  half  of  your 
money,  how  many  cents  will  you  have  left  ? 

How  many  balls  in  one-half  of  6  balls  ?  in  two- 
halves  of  6  balls  ? 

How  many  blocks  in  one-third  of  6  blocks  ?  in 
two-thirds  of  6  blocks  ?  in  three-thirds  of  6  blocks  ? 
in  three-thirds  of  3  blocks  ? 

If  a  cook  has  6  eggs,  and  uses  one-third  of  them 
for  cake,  how  many  eggs  will  be  left  ? 

A  little  boy  had  4  newspapers  to  sell,  and  he 
sold  half  of  them.    How  many  papers  had  he  left? 

How  many  pears  are  one-half  of  4  pears  and  one- 
half  of  6  pears  together  ? 


LESSON   19. 


19 


THE  J^UMBEK  SEVEN. 

Six  dots  and  one  dot  make  seven  dots. 
Here  are  seven  dots,  ///, 
We  write  the  figure  7  for  seven. 

Draw  these  cards,  and  write  7  under  each  card. 


•  •  • 

•  •  • 

• 

••• 

•     • 

• 
• 

•  • 

•  • 

• 

• 
• 

How  many  are  3  and  4  ?  4  and  3  ?  1  and  6  ? 
2  and  5  ?   6  and  2  ?   6  and  1  ? 

How  many  are  7  less  3  ?  7  less  4  ?  7  less  1  ?  7 
less  2  ?   7  less  5  ?   7  less  6  ?   7  less  7  ? 

How  many  more  are  7  chairs  than  3  chairs? 
7  balls  than  4  balls  ?  7  kittens  than  1  kitten  ?  7 
mice  than  5  mice  ?  7  ladders  than  2  ladders  ? 
7  stars  than  6  stars  ? 

How  many  dolls  must  you  put  with  3  dolls  to 
have  7  dolls  ? 

How  many  cups  must  you  put  with  4  cups  to 
have  7  cups  ? 

How  many  hats  must  you  put  with  1  hat  to  have 
7  hats  ? 

How  many  cents  must  you  put  with  2  cents  to 
have  7  cents  ? 

How  many  eggs  must  you  put  with  5  eggs  to 
have  7  eggs  ? 

How  many  cents  must  you  put  with  6  cents  to 
have  7  cents  ? 


20  LESSON   20. 

There  are  4  pigs  in  1  pen  and  3  pigs  in  another 
pen.     How  many  pigs  in  both  pens  ? 

How  many  must  you  add  to  5  to  make  7  ? 

If  you  draw  7  stars  and  rub  out  3  of  them,  how 
many  will  be  left  ?     How  many  are  7  less  3  ? 

How  many  crosses  are  6  crosses  and  1  cross  ? 

If  you  have  7  pears  and  give  away  6  of  them, 
how  many  pears  will  you  have  left  ? 

How  many  are  7  less  6  ?  7  less  1  ?  7  less  3  ?  7 
less  5  ?   7  less  2  ?   7  less  4  ? 

How  many  mittens  make  a  ^:)mr  of  mittens  ? 

How  many  boots  make  a  pair  of  boots  ? 

Here  are  7  blocks,  BiBii  liiJiiB.  Call 
them  horses,  and  find  how  many  pairs  of  horses 
you  can  have,  and  how  many  single  horses  besides  ? 

Note.  Show  the  pupils  one-cent,  two-cent,  and  five-cent  coins. 
Let  them  count  out  the  number  of  single  cents  a  two-cent  piece  equals 
in  value,  and  the  number  a  five-cent  piece  equals  in  value.  Show  the 
one-cent,  two-cent,  three-cent,  four-cent,  and  five-cent  postage  stamps. 

At  1  cent  apiece,  how  many  apples  can  you  buy 
for  a  two-cent  piece  ?   for  a  five-cent  piece  ? 

Harry  has  a  two-cent  piece  and  a  five-cent  piece. 
How  many  one-cent  postage  stamps  can  he  buy  ? 

If  you  add  1  block  to  3  times  2  blocks,  how 
many  blocks  will  you  have  ? 

How  many  are  D  D  and  D  D  ^  and  D  D  and  D  ? 

How  many  are  D  D  D  and  D  D  D  and  D  ? 

How  many  are  2  and  2  and  2  and  1  ? 

How  many  are  3  and  3  and  1  ? 


LESSON   21.  21 

Alice  has  a  five-cent  piece  and  a  two-cent  piece, 
and  Harry  has  six  cents.  How  much  more  money 
has  Alice  than  Harry  ? 

How  many  peaches  are  3  peaches  and  4  peaches  ? 

A  farmer  had  7  horses.  If  he  had  3  turned  out 
in  the  pasture,  and  the  rest  in  the  stable,  how 
many  did  he  have  in  the  stable  ? 

There  were  7  windows  in  a  room,  and  2  of  them 
were  shut.     How  many  were  open  ? 

There  were  7  eggs  in  a  basket,  but  the  cook 
used  5  of  them.     How  many  were  left  ? 

A  storekeeper  had  7  saws.  He  sold  one  saw  to 
a  carpenter.     How  many  had  he  left  ? 

A  man  had  7  cows  to  milk.  When  he  had 
milked  6  cows,  how  many  had  he  to  milk  ? 

If  one  apple  costs  1  cent,  how  much  will  7 
apples  cost  ?   5  apples  ?   3  apples  ?   6  apples  ? 

If  one  peach  costs  2  cents,  how  much  will  3 
peaches  cost  ?   2  peaches  ? 

If  you  can  buy  one  pencil  for  2  cents,  how  many 
pencils  can  you  buy  for  6  cents  ?   for  4  cents  ? 

How  many  three-cent  stamps  can  you  buy  for 
3  cents  ?  for  6  cents  ? 

George  has  7  cents.  How  many  oranges  can  he 
buy  at  3  cents  each,  and  how  many  cents  will  he 
have  left  ? 

Ellen  has  7  cents.  How  many  pears  can  she 
buy  at  2  cents  each,  and  how  many  cents  will  she 
have  left  ? 


22 


LESSON   22. 


DRILL.  EXERCISE. 

Note.  The  Teacher  may  put  the  following  groui)S  of  dots  on  the 
board,  and  call  upon  the  pupils  one  by  one  to  tell  the  number  of  dots 
as  she  touches  the  squares  at  random,  with  a  pointer.  Every  child 
should  be  carefully  drilled  on  this  exercise  until  he  can  name  each 
number  of  dots  instantly. 


_• 


•    •    • 


•  •  • 


•  •  • 

•  •  • 


•  •  • 
•  •  •  • 

•       • 

•  • 
• 

•  • 

•       • 
• 

•  •  • 
• 

•  •  • 

• 
• 

• 

•  • 

•      • 

• 

Name  two  numbers  that  together  make  4. 
Name  two  numbers  that  together  make  5. 
Name  three  numbers  that  together  make  5. 
Name  two  numbers  that  together  make  6. 
Name  three  numbers  that  together  make  6. 
Name  two  numbers  that  together  make  7. 
Name  three  numbers  that  together  make  7. 
Name  four  numbers  that  together  make  7. 
How  many  more  are  6  than  4  ?   than  3  ? 
How  many  more  are  5  than  3  ?    than  2  ? 
How  many  more  are  7  than  4  ?    than  5  ? 
How  many  more  are  7  than  3  ?    than  2  ? 


LESSON   23.  23 

THE    SIGNS  =  AND  +. 

The  sign  =  stands  for  the  word  are  or  is. 
Copy,  and  use  the  sign  that  stands  for  are  : 

1  and  12.  5  and  1         6. 

2  and  13.  2  and  5         7. 
4  and"  3         7.  3  and  2         5. 

2  and  4         6.  2  and  2         4. 

The  sign  -f  stands  for  the  word  and. 

Copy,  and  use  the  sign  that  stands  for  and : 

3  1  =  4.  3         3  =  6. 

1  2  =  3.  3         4  =  7. 

4  2  =  6.  5        2  =  7. 

2  3  =  5.  1        5  =  6. 

Copy,  and  write  each  answer  at  the  right  of  the 
sign  =  : 


1  +  1  = 

1  +  2  = 

3  +  1  = 

2  +  4  = 

1  +  4  = 

4  +  1  = 

3  +  2  = 

3  +  3  = 

1  +  5  = 

1  +  3  = 

5  +  2  = 

3  +  4  = 

2  +  2  = 

4  +  2  = 

6  +  1  = 

2  +  1  = 

1  +  6  = 

4  +  3  = 

1+1+1= 

2+2+2= 

2+ 1+ 1 = 

1  +  2  +  3  = 

2  +  2  +  1  = 

2+3+2= 

3+1+2= 

3+3+1= 

3+2+2= 

2+3+1= 

5+1+1= 

4+1+2= 

24  LESSON  24. 

THE  SIGNS   -   AND  X- 

The  sign  —  stands  for  the  word  minus. 
When  we  take  3  blocks  from  5  blocks,  we  have 
2  blocks  left. 
We  write  this, 

5  blocks  -  3  blocks  =  2  blocl^s  : 
and  we  read  this, 

5  blocks  minus  3  blocks  are  2  blocks. 

Oral  and  slate  exercises  : 

BLOCKS.  BLOCKS.  BLOCKS. 

3-1=  6-1=  6-4= 

2-1=  6-3=  5-4= 

4-2=  7-1=  7-5= 

5-3=  5-2=  7-3= 

3-2=  7-2=  7-4= 

The  sign  x  stands  for  the  word  times. 


PEARS. 

PEARS. 

PEARS. 

3x1  = 

2x3  = 

5x1  = 

2x1  = 

4x1  = 

7x1  = 

2x2  = 

6x1  = 

3x2  = 

Note.  The  pupils  should  copy  the  above,  and  similar  exercises,  on 
blocks  of  paper  or  slates,  and  write  the  answer  for  each  example. 

Also  the  Teacher  should  put  these  exercises  on  the  blackboard,  and 
with  pointer  in  hand  require  of  each  pupil  in  turn  quick  answers  to 
such  examples  as  she  touches  with  the  pointer.  One  child  at  a  time 
should  give  the  answers  aloud,  and  the  other  members  of  the  class 
should  be  on  the  alert  to  raise  their  hands  when  a  wrong  answer  is 
given.  If  a  child  gives  a  wrong  answer,  he  should  be  sent  to  the 
counting-board  to  discover  the  true  answer. 


LESSON   25.  25 

THE  DAYS  OF  THE  WEEK. 

On  what  day  of  the  week  do  we  go  to  church  ? 

The  next  day  we  come  to  school.  Who  can  tell 
the  name  of  the  day  that  follows  Sunday  ? 

Who  can  tell  the  name  of  the  day  that  follows 
Monday  ? 

What  day  comes  after  Tuesday  ? 

What  day  comes  after  Wednesday  ? 

What  day  comes  after  Thursday  ? 

The  day  that  follows  Friday  we  have  for  a  holi- 
day.    What  is  the  name  of  that  day  ? 

We  will  write  the  first  letter  of  each  day,  thus : 

S  

M 

T 

W 

T 

F  

S 

Repeat  with  me  the  days  of  the  week,  beginning 
with  Sunday. 

Wednesday  is  the  middle  day  of  the  week. 
What  day  comes  before  Wednesday  ? 
How  many  days  make  a  week  ? 
Remember  :   7  days  make  1  week. 

Note.  The  Teacher  should  make  sure  that  all  the  pupils  of  the 
class  give  close  attention  and  learn  the  days  of  the  week,  and  not  be 
satisfied  if  some  one  in  the  class  can  repeat  them.  In  fact,  this  caution 
applies  to  all  class-work. 


26 


LESSON   26. 


THE    NUMBER    EIGHT. 

Seven  dots  and  one  dot  make  eight  dots. 

Here  are  eight  dots,  J  J  J  J 

We  write  the  figure  8  for  eight. 

Copy  these  pictures  and  write  under  each  group 
the  figure  for  the  number  in  the  group  : 

xxxxxxxx  >|c>|<>)<>|c  >ic>|<  >|<)|< 

Copy  each  card  below,  and  write  under  it  the 
figure  for  the  number  of  dots  in  the  card. 


•        •  • 


•  •  • 


•  •        • 
•         •  • 

•  •     •  •  • 


•  •• 

•  ••• 


•  ••• 
•••• 


Count  the  dots  in  these  cards  from  left  to  right. 
Count  the  dots  from  right  to  left. 
What  number  follows  5  ?   follows  7  ? 
What  number  comes  before  8  ?  comes  before  5  ? 
What  number  is  between  5  and  7  ?    6  and  8  ? 
Copy,  and  add  dots  enough  to  make  8  dots  in 
each  card  below : 


X 

•  • 

•  • 

•  • 

• 
• 

• 
•  • 

•  • 

•  • 

•  • 

How  many  blocks  are  5  and  3  ?  6  and  2  ?  4  and 
3  ?   4  and  4  ?   2  and  5  ?   2  and  6  ?    7  and  1  ? 

How  many  dots  must  be  put  with  5  to  make  8  ? 
with  2  to  make  8  ?  with  3  to  make  8  ?  with  4  to 
make  8  ?   with  7  to  make  8  ?   with  6  to  make  8  ? 

How  many  more  dots  are  8  than  6  ?  8  than  3  ? 
8  than  4  ?    8  than  2  ?    8  than  1  ?   8  than  5  ? 


LESSON   27.  27 

Here  are  8  blocks,  liJB    SB    IIS    SO 

If  you  take  away  2  blocks,  how  many  will  be  left  ? 

If  you  take  away  6  blocks,  how  many  will  be  left  ? 

If  you  take  away  5  blocks,  how  many  will  be  left  ? 

If  you  take  away  3  blocks,  how  many  will  be  left  ? 

If  you  take  away  4  blocks,  how  many  will  be  left  ? 

If  you  take  away  I  block,  how  many  will  be  left  ? 

If  you  take  away  7  blocks,  how  many  will  be  left  ? 

Ellen  may  take  2  blocks  at  a  time  for  4  times. 
How  many  blocks  has  she  ?  How  many  blocks, 
then,  are  4  times  2  blocks  ? 

How  many  cups  are  4  times  2  cups  ? 

How  many  pears  are  4  times  2  pears  ? 

Erwin  may  take  4  blocks,  and  then  4  more. 
How  many  times  has  he  taken  4  blocks  ?  How 
many  blocks  has  he  ?  How  many  blocks,  then,  are 
2  times  4  blocks? 

How  many  plums  are  2  times  4  plums  ? 

How  many  apples  are  2  times  4  apples  ? 

How  many  are  4  times  2  ?  How  many  are  2 
times  4  ?   How  many  2's  in  8  ?   How  many  4's  in  8  ? 

How  many  are  3  times  2  ?  How  many  are  2 
times  3  ?   How  many  2's  in  6  ?   How  many  3's  in  6  ? 

How  many  oranges  are  one-half  of  6  oranges  ? 

How  many  apples  are  one-third  of  6  apples  ? 

When  we  take  one-half  of  6  oranges,  into  how 
many  equal  parts  do  we  divide  the  6  oranges  ? 

When  we  take  one-third  of  6  apples,  into  how 
many  eqital parts  do  we  divide  the  6  apples? 


28  LESSON  28. 

Here  are  8  blocks,  Sip    jBli    iHi    ||g 

How  many  times  must  Nora  go  to  bring  these 
blocks  to  me  if  she  brings  just  2  blocks  each  time  ? 
Then  8  blocks  divided  by  2  blocks  =  4  times. 

But  if  Nora  divides  the  blocks  into  two  equal 
parts,  how  many  blocks  will  there  be  in  each  part  ? 

Then  8  blocks  divided  by  2  =  4  blocks. 

Note,  The  Teacher  must  illustrate  in  many  ways  the  two  different 
meanings  of  Division.  When  the  divisor  is  a  mere  number,  as  2,  3,  4, 
etc.,  the  meaning  of  division  then  is  the  separation  of  the  given  num- 
ber of  things  into  2,  3,  4,  etc.,  equal  parts,  and  the  quotient  will  signify 
a  number  of  things  like  the  dividend.  When  the  divisor  is  a  number 
of  things  like  the  dividend,  the  quotient  will  signify  the  number  of 
times  the  divisor  is  contained  in  the  dividend ;  that  is,  the  number 
of  times  the  divisor  can  be  taken  from  the  dividend. 

How  many  times  are  2  cents  contained  in  6  cents  ? 
How  many  times  are  2  cents  contained  in  8  cents  ? 
How  many  times  are  4  cents  contained  in  8  cents  ? 
How  many  times  are  3  cents  contained  in  6  cents  ? 

What  is  the  answer  for 

8  cents  divided  by  4  cents  ? 
8  pears  divided  by  2  pears  ? 
6  peaches  divided  by  2  peaches  ? 
6  plums  divided  by  3  plums  ? 
8  chairs  divided  by  2  chairs  ? 
8  oranges  divided  by  4  oranges  ? 

This  sign  -t-  stands  for  the  words  divided  by. 


4  dogs  -^  2  =  ? 

6  pears  -^  3  = 

4  hens  ^  2  =  ? 

8  cents  -^  2  = 

6  figs    ^2  =  ? 

8  tops    ^  2  = 

LESSON   29.  29 

Divide  these  eight  dots  tlms,  ••/••/••/•• 

Into  how  msiny  equal  partshsive  you  divided  them  ? 

If  a  number  of  things  is  divided  into  four  equal 
parts,  each  part  is  one-fourth  of  the  number. 

How  many  dots  in  one-fourth  of  8  dots  ? 

How  many  dots  in  two-fourths  of  8  dots  ? 

How  many  dots  in  three-fourths  of  8  dots  ? 

How  many  dots  in  four-fourths  of  8  dots  ? 

How  many  dots  in  one-half  of  8  dots  ? 

How  many  dots  in  two-halves  of  8  dots  ? 

Fourths  are  often  called  quarters. 

Find  one-quarter  of  4  dollars ;    of  8  cents. 

Find  two-quarters  of  4  dollars  ;  of  8  cents. 

Find  three-quarters  of  4  dollars ;  of  8  cents. 

Find  four-quarters  of  4  dollars ;    of  8  cents. 

Find  one-half  of  4  dollars  ;  of  8  cents  ;  of  8  pigs. 

What  part  of  8  blocks  are  4  blocks  ?  are  2  blocks  ? 

What  part  of  8  cents  are  2  cents  ?  are  4  cents  ? 

What  part  of  6  cups  are  3  cups  ?   are  2  cups  ? 

Which  is  greater,  one-half  of  8  cents  or  one-fourth 
of  8  cents  ?  one-half  of  8  cents  or  one-quarter  of  8 
cents  ? 

Which  is  greater,  one-half  of  8  cents  or  two- 
fourths  of  8  cents  ?  one-half  of  8  cents  or  three- 
fourths  of  8  cents  ? 

Here  is  a  new  way  of  writing  one-half,  thus,  ^  ; 
one-third,  thus,  i  ;  one-fourth,  thus,  i. 

We  write  two-thirds,  thus,  §  ;  two-fourths,  thus, 
i ;  three-quarters,  thus,  f . 


30 


LESSON   30. 


Read  :i;i;i;i;|;l;1 
Write    in   figures  :    one-half ; 


one-third  :    two- 


thirds  ;  one-fourth ;  three-quarters. 
Oral  and  slate  exercises  : 


5  +  2  = 

7-2  = 

7-5  = 

5  +  3  = 

8-5  = 

8-3  = 

6  +  2  = 

8-6  = 

8-2  = 

7  +  1  = 

8-1  = 

8-7  = 

2  +  2  = 

3  +  3  = 

4  +  4  = 

4-2  = 

6-3  = 

8-4  = 

2x2  = 

2x3  = 

3x2  = 

4-^-2  = 

6^3  = 

6^2  = 

2x4  = 

4x2  = 

8-^2  = 

8^4  = 

hoi  4:  = 

iof6  = 

iof  8  = 

^of  6  = 

lof8  = 

iof8  = 

ORSKS. 

iof8  = 

§of  6  = 

COLTS 

H 

MULES. 

4  + 

=  7. 

5  +         =8. 

7- 

=  3 

4  + 

=  8. 

7+        =8. 

8- 

=  4 

4  + 

=  6. 

6+         =8. 

8- 

=  1 

4x 

=  8. 

3+         =8. 

8- 

=  6 

2x 

=  8. 

4+         =6. 

8^ 

=  4 

3x 

=  6. 

8-        =5. 

6^ 

=  3 

2x 

=  6. 

8-        =7. 

8^ 

=  2 

2x 

=  4. 

8-        =3. 

6-^ 

=  2 

5x 

=  5. 

8-        =2. 

4^ 

=  2 

LESSON   31.  31 


If  a  melon  is  cut  into  four  equal  parts,  what  is 
one  of  the  parts  called  ? 

What  are  three  of  the  parts  called  ? 

How  many  quarters  of  a  melon  does  it  take  to 
make  a  whole  melon  ? 

How  many  quarters  of  a  melon  does  it  take  to 
make  half  of  a  melon  ? 

How  many  quarters  of  a  dollar  does  it  take  to 
make  a  dollar  ?  to  make  half  of  a  dollar  ? 

How  many  quarters  of  a  dollar  does  it  take  to 
make  2  dollars  ? 

How  many  quarters  of  a  dollar  does  it  take  to 
make  one  dollar  and  a  half  ? 

How  many  quarters  of  a  dollar  does  it  take  to 
make  one  dollar  and  a  quarter  ? 

If  Sbjpie  is  cut  into  quarters,  and  Mary,  Tom,  and 
Harry  each  have  a  quarter,  how  many  quarters 
will  be  left  for  Alice  ? 

If  half  of  a  pie  is  cut  into  two  equal  parts,  what 
part  of  the  ivhole  pie  is  each  piece  ? 

What  part  of  the  whole  pie  are  the  two  pieces 
together  ? 

How  many  fourths  make  one-half  ? 


32  LESSON   32. 


Which  one  of  these  measures  is  the  smallest  ? 
How  many  gills  will  the  pint  measure  hold  ?  * 
Then  four  gills  make  one  pint. 
At  1  cent  a  gill,  what  will  a  pint  of  milk  cost  ? 
At  2  cents  a  gill,  what  will  a  pint  of  syrup  cost? 
How  many  gills  in  a  half  pint  of  water  ? 

How  many  pints  will  the  quart  measure  hold  ?  * 

Then  two  pints  make  one  quart. 

At  4  cents  a  pint,  what  will  a  quart  of  milk  cost  ? 

At  3  cents  a  pint,  what  will  a  quart  of  oil  cost  ? 

At  6  cents  a  quart,  what  will  a  pint  of  berries  cost  ? 

What  part  of  a  quart  is  1  pint  ? 

How  many  gills  make  1  quart  ? 

How  many  quarts  will  the  gallon  measure  hold  ?  * 

Then  four  quarts  make  one  gallon. 

How  many  quart  cans  are  needed  for  a  gallon 
of  milk  ?     How  many  two-quart  cans  ? 

At  2  cents  a  quart,  what  will  a  gallon  of  skim- 
milk  cost  ?     What  will  a  half-gallon  cost  ? 

What  part  of  a  gallon  is  one  quart  ? 

What  part  of  a  gallon  are  2  quarts  ?  are  3  quarts  ? 

At  8  cents  a  gallon,  what  will  a  quart  of  skim- 
milk  cost  ?     What  will  a  pint  cost  ? 

Note.*   Let  the  pupil  discover  by  trial  the  answer  to  this  question. 


LESSON   33. 


33 


THE  NUMBER  NINE. 

Eight  dots  and  one  dot  make  nine  dots. 

Here  are  nine  dots,  ••• 

•  •• 

We  write  the  figure  9  for  nine. 

Copy  these  pictures,  and  write  under  each  group 
the  figure  for  the  number  in  the  group  : 

///////// 


*  * 

*  *  * 

*  *  *  * 


X  X  X  X 
X  X  X  X  X 


O0OOOOOOO 
Copy  these  cards,  and  add  dots  enough  to  make 
9  dots  in  each  card,  and  write  9  under  each  card  : 


• 

• 
• 
• 

• 
• 
• 
• 

• 
• 

•  • 

•  • 

•  • 

••• 
•••• 

•••• 
•••• 

•  • 
• 

•  • 

How  many  dots  are  3  and  6  ?  5  and  4  ?  7  and 
2  ?  1  and  8  ?  3  and  3  ?  2  and  7  ?  4  and  3  ?  4 
and  5  ?   4  and  4  ?   6  and  3  ?   8  and  1  ?   5  and  3  ? 

How  many  dots  must  you  put  with  5  to  make  9  ? 

How  many  dots  must  you  put  with  2  to  make  9  ? 

How  many  dots  must  you  put  with  3  to  make  9  ? 

How  many  dots  must  you  put  with  4  to  make  9  ? 

How  many  dots  must  you  put  with  6  to  make  9  ? 

How  many  dots  must  you  put  with  8  to  make  9  ? 

How  many  dots  must  you  put  with  7  to  make  9  ? 

How  many  more  dots  are  9  than  7  ?  9  than  6  ? 
9  than  3  ?   9  than  4  ?    9  than  5  ?   9  than  2  ? 


34 


LESSON   34. 


Here  are  9  blocks,  SfBH  BBB  181811 
If  you  take  away  3  blocks,  how  many  will  be  left  ? 
If  you  take  away  6  blocks,  how  many  will  be  left  ? 
If  you  take  away  5  blocks,  how  many  will  be  left  ? 
If  you  take  away  4  blocks,  how  many  will  be  left  ? 
If  you  take  away  7  blocks,  how  many  will  be  left  ? 
If  you  take  away  2  blocks,  how  many  will  be  left  ? 
If  you  take  away  1  block,  how  many  will  be  left  ? 
If  you  take  away  8  blocks,  how  many  will  be  left  ? 
How  many  are  : 


8  minus  2  ? 
8  minus  6  ? 
8  minus  5  ? 
8  minus  4  ? 
8  minus  7  ? 


9  minus  3  ? 
9  minus  6  ? 
9  minus  7  ? 
9  minus  8  ? 
9  minus  2  ? 


7  minus  4  ? 
7  minus  6  ? 
7  minus  3  ? 
7  minus  2  ? 
7  minus  5  ? 


9  minus  4  ? 
9  minus  5  ? 

8  minus  3  ? 

9  minus  1  ? 
6  minus  4  ? 


Emma  may  take  3  blocks  at  a  time  for  3  times. 
How  many  blocks  has  Emma  ? 
How  many  blocks,  then,  are  3  times  3  blocks  ? 
How  many  peaches  are  3  times  3  peaches  ? 
How  many  roses  are  3  times  3  roses  ? 
How  many  lambs  are  3  times  3  lambs  ? 
How  many  are  3  times  3  ? 
Here  are  9  pears,  e^  C^  ^    ddd    ddd 
How  many  times  can  you  take  3  pears  from  the  9  ? 
How  many  groups  of  3  pears  each  can  you  make 
from  the  9  ? 

9  pears  divided  by  3  pears  gives  how  many  times  ? 
9  pears  divided  by  3  gives  how  many  pears  ? 
How  many  pears  are  3  of  9  pears  ? 


LESSON   35.  36 

Here  are  9  dots,  ••••••••• 

Put  your  pencil  between  the  second  and  third 
dots.  How  many  dots  are  on  the  left  of  the  pen- 
cil ?     How  many  on  the  right  of  the  pencil  ? 

Put  your  pencil  between  the  fourth  and  fifth 
dots.  How  many  dots  are  on  the  left  of  the  pen- 
cil ?     How  many  on  the  right  of  the  pencil  ? 

Put  your  pencil  between  the  fifth  and  sixth  dots. 
How  many  dots  on  the  left  ?  How  many  dots  on 
the  right  ? 

If  a  boy  goes  up  8  steps  2  steps  at  a  time,  how 
many  steps  will  he  touch  ? 

John  had  9  flags,  some  of  them  red  and  the  rest 
blue.    If  4  of  them  were  red,  how  many  were  blue  ? 

Alice  had  9  cents,  and  spent  3  cents.  How 
many  had  she  left  ? 

George  sells  a  newspaper  for  2  cents,  and  receives 
a  five-cent  piece  in  payment.  How  many  cents 
must  he  give  back  ? 

A  hen  had  9  chickens,  but  a  hawk  caught  2. 
How  many  chickens  were  left  ? 

Miriam  has  8  cents,  and  Hattie  3  less  than 
Miriam.     How  many  cents  has  Hattie  ? 

Harry  has  3  tops,  and  Tom  has  6  more  than 
Harry.     How  many  tops  has  Tom  ? 

I  wanted  8  stamps  for  my  letters,  and  had  only 
3.     How  many  more  must  I  buy  ? 

Tom  had  6  apples,  and  gave  away  a  of  them. 
How  many  had  he  left  ? 


36  LESSON   36. 

Florence  had  8  apples  on  plates,  2  on  a  plate.  How 
many  plates  were  there  ?    How  many  twos  in  eight  ? 

Annie  had  8  pears  on  plates,  4  on  a  plate.  How 
many  plates  were  there  ?    How  many  fours  in  eight  ? 

Hattie  had  9  peaches,  3  on  a  plate.  How  many 
plates  were  there  ?     How  many  threes  in  9  ? 

8^2=  8^4=  9^3= 

i  of  8  =  i  of  8  =  ^  of  9  = 

Mary  had  3  rows  of  buttons,  3  in  a  row.  How 
many  buttons  had  she  ? 

If  one  orange  costs  3  cents,  what  will  2  oranges 
cost  ?     What  will  3  oranges  cost  ? 

If  a  quart  of  milk  costs  6  cents,  what  will  a  pint 
cost  ?     What  will  3  pints  cost  ? 

If  a  pint  of  vinegar  costs  4  cents,  what  will  a 
gill  cost  ?     What  will  a  quart  cost  ? 

If  a  pint  of  water  will  fill  4  gill  cups,  how  many 
gill  cups  will  a  quart  of  water  fill  ? 

If  a  quart  of  milk  will  fill  2  pint  cups,  how  many 
pint  cups  will  a  gallon  of  milk  fill  ? 

How  many  quart  measures  will  a  one-gallon  can 
of  milk  fill  ?   will  a  two-gallon  can  fill  ? 

A  cook  had  9  eggs,  and  used  h  of  them  for  a 
pudding.     How  many  eggs  were  left  ? 

Harry  had  8  oranges.  He  gave  one-quarter  of 
them  to  his  sister  Mary,  one-quarter  of  them  to  his 
sister  Alice,  and  one-quarter  of  them  to  his  sister 
Ellen.     How  many  did  he  keep  for  himself  ? 


LESSON   37. 


3T 


Oral  and  slate  exercises  : 


FIGS. 

BELLS. 

APPLES. 

2  +  7  = 

9-2  = 

9-7  = 

4  +  5  = 

9-4  = 

9-5  = 

3  +  5  = 

8-3  = 

8-5  = 

3  +  6  = 

9-3  = 

9-6  = 

5  +  2  = 

7-5  = 

7-2  = 

4  +  3  = 

7-3  = 

7-4  = 

1  +  8  = 

9-6  = 

9-8  = 

4  +  2  = 

6-4  = 

6-2  = 

4  +  4  = 

6  -  3  = 

8-4  = 

3x3  = 

iof4  = 

iof6  = 

hoi  2  = 

J  of  3  = 

Jof  6  = 

J  of  9  = 

iof8  = 

iof8  = 

SLEDS. 

ORANGES. 

LAMBS. 

4  =  1  + 

6   =   4   + 

8  =  3  + 

4  =  2  + 

7  =  1  + 

8  =  4  + 

4  =  3  + 

7  =  4  + 

8  =  5  + 

5  =  1  + 

7  =  5  + 

9  =  1  + 

5  =  3  +  - 

7  =  3  + 

9  =  8  + 

5  =  4  + 

7  =  6  + 

9  =  2  + 

5  =  2  + 

7  =  2  + 

9  =  7  + 

6  =  3  + 

8=1  + 

9  =  3  + 

6  =  1  + 

8  =  6  + 

9  =  6  + 

6  =  2  + 

8  =  7  + 

9  =  4  + 

6  =  5  + 

8  =  2  + 

9  =  5  + 

Note.  Besides  copying  and  completing  these  and  similar  exercises, 
the  oral  drill  must  be  kept  up  until  every  one  of  the  class  can  give  the 
answers  promptly. 


38  LESSON   38. 

THE    FIGURE    ZERO. 

The  figure  0  is  called  zero,  naught,  or  cipher. 

The  figure  0  means  none  to  count. 

Four  roses  grew  on  a  bush ;  2  were  picked ;  and 
then  2  more.  Write  the  figure  for  the  number  left. 

Write  the  figure  for  the  number  of  blocks  left 
when  you  take  away  5  blocks  from  5  blocks. 

Write  the  figure  for  the  number  of  oranges  left 
if  you  had  4  oranges  and  gave  them  all  away. 


Review  of  figures : 

You  have  now  had  all  the  figures  used  for  writ- 
ing numbers,  and  have  learned  the  meaning  of  each 
separate  figure.     Thus : 

The  figure  1  is  written  for  One. 
The  figure  2  is  written  for  Two. 
The  figure  3  is  written  for  Three. 
The  figure  4  is  written  for  Four. 
The  figure  5  is  written  for  Five. 
The  figure  6  is  written  for  Six. 
The  figure  7  is  written  for  Seven. 
The  figure  8  is  written  for  Eight. 
The  figure  9  is  written  for  Nine. 
The  figure  O  is  written  for  None. 

Draw  a  square,  and  write  0  under  it :  then  an- 
other square,  and  write  1  under  it ;  and  so  on  to  9. 

Put  in  each  square  the  number  of  dots  indicated 
by  the  figure  written  under  it. 


LESSON   39. 


39 


THE  NUMBER  TEN. 

Nine  dots  and  one  dot  make  ten  dots. 
Here  are  ten  dots,  2  J  J  J  J 
We  write  the  figures  10  for  ten. 


I 


Ten  ones  make  1  ten. 

Draw  these  number  pictures  of  ten,  and  write 
under  each  division  the  figure  for  the  number  of 
dots  in  the  division  : 


•  •  • 

•  •  • 

•  •  • 

• 

.... 

•  •  •  • 

• 
• 

•  •  •       • 

•           • 

•  •  •       • 

9  +  1 

•  •  • 

•  •  • 

•  • 

•  • 

•  • 
• 

•  • 

•  • 
• 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

• 
• 
• 

•  •  • 
• 

•  •  • 

• 
• 

•  •  •  • 

•  •  •  • 

• 

•  •  • 

•  •  • 

•  •  • 

Look  at  these  number  cards,  and  answer  the  fol- 
lowing questions  : 

How  many  must  you  add  to  9  to  make  10  ?  to 
8  to  make  10  ?  to  7  to  make  10  ?  to  6  to  make 
10  ?  to  5  to  make  10  ?  to  4  to  make  10  ?  to  3  to 
make  10  ?   to  2  to  make  10  ?   to  1  to  make  10  ? 

How  many  more  are  10  than  2  ?  than  4  ?  than  6  ? 
than  8  ?   than  3  ?   than  5  ?   than  7  ?    than  9  ? 


40  LESSON  40. 

John  found  3  eggs  on  Thursday,  and  4  on  Friday. 
How  many  eggs  did  he  find  ? 

There  are  7  days  in  a  week.  When  2  are  gone, 
how  many  are  left  ? 

There  were  7  red  roses  on  a  rose  bush,  and  5 
white  roses  on  another  bush.  How  many  more 
red  roses  were  there  than  white  roses  ? 

Susan  had  3  apples,  and  James  had  5  apples. 
How  many  apples  had  Susan  and  James  together  ? 

Alice  had  8  dolls,  and  gave  away  3  of  them. 
How  many  had  she  left  ? 

If  a  window  has  4  panes  of  glass,  how  many 
panes  of  glass  in  2  windows  ? 

How  many  feet  have  2  dogs  ?  4  hens  ? 

If  you  take  2  apples  4  times  from  a  dish  that 
has  8  apples  in  it,  how  many  apples  will  be  left  ? 

There  were  8  rooms  in  a  house,  half  of  them  in 
the  first  story,  and  half  in  the  second  story.  How 
many  were  there  in  each  story  ? 

John  had  8  peaches,  and  gave  aw^ay  a  quarter 
of  them.     How  many  peaches  did  he  give  away  ? 

Frank  bought  9  marbles,  and  gave  away  4  of 
them.     How  many  had  he  left  ? 

There  are  9  apples  in  a  dish.  How  many  boys 
can  have  3  apples  apiece  ? 

At  3  cents  apiece,  how  many  oranges  can  you 
buy  for  6  cents  ?  for  9  cents  ? 

At  2  cents  apiece,  how  many  pears  can  you  buy 
for  9  cents,  and  how  many  cents  will  be  left  ? 


i 


Part  II. 


LESSON   1. 


10 


a 

1 


1   2 


Look  at  the  number  picture  on  the  right.  What 
do  you  see  over  the  2  ?  2  ones.  Over  the  1  ? 
1  ten.     Then  12  means  one  ten  and  two  ones. 

Look  at  the  middle  number.  What  do  you  see 
over  the  1  at  the  right  ?  What  do  you  see  over 
the  1  at  the  left  ?    Then  1 1  means  one  ten  and  one. 

Look  at  the  number  picture  on  the  left.  What 
do  you  see  over  the  0  ?  What  do  you  see  over  the 
1  ?     Then  10  means  one  ten  and  no  ones. 

Note.  The  Teacher  should  proceed  in  Part  II.  as  in  Part  I. ;  show- 
ing objects,  drawing  number  pictures  on  the  board,  and  reading  all 
the  clothed  exercises  for  the  pupils.  Pupils  should  have  the  books 
simply  to  copy  and  solve  the  numerical  exercises. 

41 


42  LESSON   2, 

John  may  go  to  the  counting-board.  How  many 
holes  are  there  in  the  top  row  ?  Put  one  nail  in 
one  of  the  holes  of  the  top  row. 

How  many  holes  are  left  in  the  row  ? 

Then  how  many  must  we  add  to  1  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  are  there 
now  ?     How  many  holes  are  left  in  the  row  ? 

Then  how  many  must  we  add  to  2  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  are  there 
now  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  3  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  are  there 
now  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  4  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  in  the 
row  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  5  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  in  the 
row  ?     How  many  holes'  are  left  in  the  row  ? 

How  many  must  we  add  to  6  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  in  the 
row  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  7  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  are  there 
now  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  8  to  make  10  ? 

Put  in  one  more  nail.  How  many  nails  now  in 
the  row  ?     How  many  holes  are  left  in  the  row  ? 

How  many  must  we  add  to  9  to  make  10  ? 


LESSON   3.  43 

Here  are  ten  rings,  OOOOOOOOOO 

I  will  put  the  end  of  the  pointer  between  the 
second  and  third  rings. 

How  many  rings  on  the  left  of  the  pointer  ? 

How  many  rings  on  the  right  of  the  pointer  ? 

How  many  are  2  and  8  ? 

How  many  are  10  less  2  ?    10  less  8  ? 

I  will  put  the  end  of  the  pointer  between  the 
third  and  fourth  rings. 

How  many  rings  on  the  left  of  the  pointer  ? 

How  many  rings  on  the  right  of  the  pointer  ? 

How  many  are  3  and  7  ? 

How  many  are  10  less  3  ?    10  less  7  ?     , 

I  will  put  the  end  of  the  pointer  between  the 
fourth  and  fifth  rings. 

How  many  rings  on  the  left  of  the  pointer  ? 

How  many  rings  on  the  right  of  the  pointer  ? 

How  many  are  4  and  6  ? 

How  many  are  10  less  4  ?    10  less  6  ? 

I  will  put  the  end  of  the  pointer  between  the 
fifth  and  sixth  rings. 

How  many  rings  on  the  left  of  the  pointer  ? 

How  many  rings  on  the  right  of  the  pointer  ? 

How  many  are  5  and  5  ? 

How  many  are  10  less  5  ? 

How  many  are  10  less  1  ?    10  less  9  ? 

Note.  Practise  this  exercise,  putting  the  pointer  in  different  posi- 
tions, until  the  pupils  can  readily  name  any  two  parts  of  10,  and  the 
part  left  when  one  part  is  taken  from  10. 


44 


LESSON   4. 


In  each  of  the  number  pictures  below,  the  bundle 
is  a  bundle  of  ten. 

Write  the  figures  for  the  number  in  each  case. 

I     II     III 

How  many  figures  do  you  write  for  each  number  ? 
What  does  the  figure  on  the  left  show  ? 
What  does  the  figure  on  the  right  show  ? 
What  is  the  number  11  called  ?   Eleven. 
What  is  the  number  12  called  ?   Twelve. 

Note.  It  is  absolutely  necessary  for  the  Teacher  to  show  bundles 
of  ten  things  (pencils,  sticks,  etc.)  kept  distinct  by  rubber  bands, 
in  order  to  show  the  compositions  of  numbers  containing  tens  and 
ones ;  and  to  show  also  that  the  counting  of  units  of  tens  is  exactly 
the  same  as  the  counting  of  single  units. 

Oral  and  slate  exercises  : 


8  +  ?=  10. 

6  +  ?  =  10. 
5  +  ?  =  10. 

1  +  ?=  10. 

3  +  ?  =  10. 

7  +  ?  =  10. 

2  +  ?  =  10. 

4  +  ?=  10. 

9  +  ?=  10. 


5=1  +  ? 

5  =  2  +  ? 
4  =  2  +  ? 
4  =  1  +  ? 

6  =  1  +  ? 
6  =  3  +  ? 

6  =  4  +  ? 

7  =  6  +  ? 
7  =  4  +  ? 


7  =  5  +  ? 

7  =  3  +  ? 

8  =  2  +  ? 
8  =  3  +  ? 

8  =  4  +  ? 

9  =  3  +  ? 
9  =  5  +  ? 
9  =  2  +  ? 
9  =  8  +  ? 


I 


Note.  Continue  these  oral  and  slate  exercises  until  every  pupil 
can  separate  10  into  any  two  parts,  and  see  at  a  glance  the  number  to 
be  added  to  any  part  to  make  10  ;  and  also  see  the  part  required  when] 
a  number  less  than  10  and  one  of  its  parts  is  given. 


LESSON   5.  46 

There  were  5  birds  in  a  tree,  and  5  more  flew  in 
the  tree.     How  many  birds  were  in  the  tree  then  ? 

A  teamster  has  5  teams  of  2  horses  each.  How 
many  horses  has  he  ? 

Harry  brought  in  some  wood  twice.  The  first 
time  he  brought  in  4  sticks,  and  the  next  time  5 
sticks.     How  many  sticks  did  he  bring  in  ? 

There  are  4  plates  on  each  side  of  a  table,  and 
one  plate  at  each  end.     How  many  plates  in  all  ? 

If  a  table  is  3  feet  long  and  2  feet  wide,  how 
many  feet  long  are  the  2  sides  and  2  ends  together  ? 

A  farmer  brought  10  bushels  of  potatoes  to  put 
into  his  cellar.  After  he  had  put  in  6  bushels,  how 
many  more  bushels  remained  to  be  put  in  ? 

Daisy  has  10  chickens.  Five  are  white,  and  the 
rest  brown.     How  many  are  brown  ? 

A  room  is  10  feet  high,  and  the  top  of  the  door 
is  7  feet  from  the  floor.  How  many  feet  from  the 
top  of  the  door  is  the  ceiling  ? 

There  were  10  saucers  and  only  8  cups.  How 
many  saucers  were  without  cups  ? 

I  have  10  letters  to  mail,  and  only  1  stamp. 
How  many  stamps  must  I  buy  ? 

If  a  boy  has  10  apples,  and  eats  2  apples  a  day, 
how  many  days  will  they  last  ? 

If  a  boy  has  10  cents,  and  spends  half  of  them, 
how  many  will  he  have  left  ? 

Note,  These  and  similar  questions  can  be  made  more  intelligible 
and  interesting  by  illustrating  them  with  suitable  number  pictures. 


46 


LESSON   6. 


B 

11 

ELEVEN 


•  •             « 

•  •             t 

• 
• 

• 

— 

•  •    • 

•  •    • 

•  •     • 

•  •    • 

12 

TWELVE 


13 

THIRTEEN 


14 
FOURTEEN 


15 
FIFTEEN 


How  many  dots  are  10  dots  and  1  dot  ?  10  dots 
and  2  dots  ?  10  dots  and  3  dots?  10  dots  and  4 
dots  ?    10  dots  and  5  dots  ? 

How  many  sheep  are  10  sheep  and  1  sheep  ? 
10  sheep  and  2  sheep  ?  10  sheep  and  3  sheep  ?  10 
sheep  and  4  sheep  ?    10  sheep  and  5  sheep  ? 

If  you  have  10  oranges,  how  many  more  must 
you  buy  to  have  13  ?   to  have  14  ? 

How  many  blocks  must  you  add  to  10  blocks  to 
have  15  ?   to  have  12  ?   to  have  11  ? 

How  many  twos  are  there  in  8  ?   in  10  ? 

Oral  and  slate  exercises : 


10  +  1  =  ? 
10  +  3  =  ? 
10  +  5  =  ? 
10  +  2  =  ? 
10  +  4  =  ? 


11  -  1  =  ? 

13  -  3  =  ? 
15-5  =  ? 
12-2  =  ? 

14  -  4  =  ? 


CHICKKNS. 

11-10  =  ? 

13  -  10  =  ? 
15-10  =  ? 
12  -  10  =  ? 

14  -  10  =  ? 


LESSON   7. 


47 


•  •  •  •  9_     9 

•  •  •  _?.    ^  JL    -^ 

•  •  •*  *_?.  •       ♦ 

•  ••  _?_-?_  —    —  —    — 

•  •  ••  ••  ••  9^     9_ 

•  •  ••  ••  ••  •      9_ 

•  •  ••  ••  ••  •• 

•  •  ••  ••  ••  •• 

ZH      S^  SB  BS  —  k 


16 

17 

18 

19 

20 

SIXTEEN 

SEVENTEEN 

EIGHTEEN 

NINETEEN 

TWENTY 

How  many  dots  are  10  dots  and  6  dots  ?  10  dots 
and  7  dots  ?  10  dots  and  8  dots  ?  10  dots  and  9 
dots  ?    10  dots  and  10  dots  ? 

If  you  have  10  cards,  how  many  more  must  you 
have  to  make  16  cards  ?   to  make  17  cards  ? 

How  many  marbles  must  you  put  with  10  mar- 
bles to  make  19  marbles  ?   to  make  18  marbles  ? 

How  many  cents  have  you  if  you  have  10  cents, 
5  cents,  and  1  cent  ? 

How  many  cents  have  you  if  you  have  ten  cents, 
five  cents,  and  two  cents  ? 

Oral  and  slate  exercises  : 


CROWS. 

10  +  7  =  ? 
10+  9  =  ? 
10  +  6  =  ? 
10+  8  =  ? 
10  +  10  =  ? 


17-  7  =  ? 
19-  9  =  ? 
16  -    6  =  ? 

18-  8  =  ? 
20  -  10  =  ? 


17  -  10  =^  ? 
19  -  10  =  ? 
16  -  10  =  ? 

18  -  10  =  ? 
15-10  =  ? 


48  LESSON   8. 

Write  under  the  number  pictures  below  the  fig- 
ures for  the  number,  and  the  name  of  the  number. 

II  III  nil  mil  I 

In  which  place  do  we  write  the  ones  ?    the  tens  ? 

Note.  Tupils  should  be  made  familiar  with  the  dime  and  all  coins 
of  smaller  value  ;  and  with  the  ten-cent  postage  stamp,  and  all  stamps 
of  smaller  value. 

Annie  has  2  five-cent  pieces  and  a  one-cent  piece. 
How  much  money  has  Annie  ?     2x5  +  1  =  ? 

What  two  pieces  of  money  together  make  11 
cents  ?     10  -f- 1  -=  ? 

What  two  pieces  of  money  together  make  12 
cents  ?     10  +  2  -  ? 

What  two  pieces  of  money  together  make  15 
cents  ?     10  +  5  =  ? 

Alice  has  2  five-cent  pieces  and  a  two-cent  piece. 
How  much  money  has  Alice  ?     2x5  +  2  =  ? 

Harry  has  3  five-cent  pieces.  How  much  money 
has  Harry  ?     5  +  5  +  5  -  ? 

What  five  pieces  of  money  together  make  14 
cents  ?     5  +  5  +  2  +  1 +  1-? 

What  three  pieces  of  money  together  make  13 
cents  ?     10  +  2  +  1  --  ? 

What  four  pieces  of  money  together  make  13 
cents  ?     5  +  5  +  2  +  1  =  ? 

What  four  pieces  of  money  together  make  14 
cents  ?     5  +  5  +  2  +  2  =  ? 


I 


LESSON  9.  49 

Write  under  the  number  pictures  below  the  fig- 
ures for  the  number,  and  the  name  of  the  number. 


In  which  place  do  we  write  the  ones  ?   the  tens  ? 

How  many  tens  and  how  many  ones  are  there 
in  16?   in  17?   in  18?   in  19? 

How  many  ones  must  we  add  to  9  ones  to  make 
1  ten  f  to  7  ones  to  make  1  ten  f  to  6  ones  to 
make  1  ten  f   to  8  ones  to  make  1  ten  f 

How  many  tens  and  how  many  ones  in  20  ? 

What  does  the  figure  0  mean  in  the  number  20  ? 

How  many  twos  in  10?     XX  XX  XX  XX  XX 

How  many  fives  in  10  ?     XXXXX     XXXXX 

How  many  more  twos  in  16  than  in  10  ?  How 
many  twos  in  16  ? 

How  many  more  twos  in  18  than  in  10  ?  How 
many  twos  in  18  ?     How  many  twos  in  12  ? 

How  many  more  ones  in  19  than  in  17  ? 

How  many  more  ones  in  19  than  in  16  ? 

How  many  more  ones  in  19  than  in  10  ? 

How  many  more  ones  in  18  than  in  10  ? 

How  many  more  ones  in  16  than  in  10  ? 

How  many  more  ones  in  17  than  in  10  ? 

How  many  more  ones  in  18  than  in  16  ? 

How  many  more  ones  in  15  than  in  10  ? 

How  many  more  ones  in  15  than  in  12  ? 


50  LESSON  10. 
Oral  and  slate  exercises  : 

SHEEP.                                                    LAMBS.  MEN. 

12  +  2  =  ?                11  +  2  =  ?  13  +  3  =  ? 

11  +  4  =  ?                15  +  2  =  ?  14  +  3  =  ? 

14  +  5  =  ?                13  +  4  =  ?  12  +  6  =  ? 
16  +  3  =  ?                14  +  2  =  ?  17  +  1  =  ? 

12  +  4  =  ?                12  +  5  =  ?  11  +  8  =  ? 

13  +  6  =  ?                11  +  7  =  ?  15  +  3  =  ? 

15  +  4  =  ?               17  +  2  =  ? 
18  +  1  =  ?               12  +  3  --  ?  11  +  3 
12  +  7  -=  ?               11  +  6  =  ?  14  +  4 


17  -  1  -=  ?  15  -  3  -  ?  14  -  2  =  ? 

13  -  2  --  ?  19  -  4  -  ?  18  -  6  -  ? 
19  -  5  =  ?  19  -  7  =  ?  16  -  5  =  ? 

16  -  2  =  ?  14  -  2  =  ?  19  -  4  -  ? 
19  -  6  -  ?  17  -  3  -  ?  18  -  4  =  ? 

14  -  3  =  ?  19  -  2  -^  ?  16  -  4  -=  ? 
15 -2-?  17-4==?  19-8  =  ? 

17  -  5  =  ?  18  -  5  -  ?  17  -  2  =  ? 
16-3  =  ?  19-3  =  ?  18~1  =  ? 

Note.  The  above  exercises,  and  similar  exercises,  should  be  worked 
aloud  by  each  one  of  the  class  in  turn ;  and  on  blocks  of  paper  or 
slates.  Thus,  the  first  example  should  be  worked  at  first,  as  follows  : 
12  sheep  and  2  sheep  are  14  sheep. 

If  a  child  makes  a  mistake,  let  the  child  himself  correct  it  by  the 
counting-board  or  by  dots  on  the  blackboacd.  Care  should  be  taken 
to  have  him  clearly  see  that  these  operations  are  confined  to  the  ones. 
Thus,  in  adding  2  to  12,  let  him  fill  the  top  row  of  holes  in  the  coinit- 
ing-board  with  nails,  and  2  holes  more  in  the  next  row  for  the  12,  tlien 
put  two  more  nails  in  the  row  with  the  2  nails  already  there.  He  will 
then  see  that  12  +  2  =  10  +  4  =  14. 


A 


LESSON   11.  51 

How  many  cents  are  12  cents  and  5  cents  ? 

How  many  days  are  1  week  and  3  days  ? 

How  many  inches  are  11  inches  and  7  inches  ? 

How  many  boys  are  13  boys  and  6  boys  ? 

How  many  pinks  are  15  pinks  and  3  pinks  ? 

One  rose-bush  has  17  roses,  and  another  only  2. 
How  many  have  both  bushes  together  ?  How 
many  more  has  one  bush  than  the  other  ? 

A  farmer  has  16  cows  in  the  barn,  and  3  in  the 
stable.  How  many  cows  has  he  in  all  ?  How 
many  more  in  the  barn  than  in  the  stable  ? 

A  man  has  14  work  horses  and  2  driving  horses. 
How  many  horses  has  he  ?  How  many  more  work 
horses  than  driving  horses  ? 

James  found  15  eggs  in  one  nest,  and  5  in  an- 
other.    How  many  eggs  did  he  find  in  both  nests  ? 

The  number  12  is  sometimes  called  a  dozen. 

When  we  say  a  dozen  eggs,  we  mean  tivelve  eggs. 

Frank  started  with  a  dozen  eggs  from  the  barn, 
Ijut  dropped  and  broke  two  before  he  reached  the 
house.     How  many  did  he  carry  into  the  house  ? 

John  has  a  dozen  chickens  of  one  kind,  and  6  of 
another  kind.     How  many  has  he  of  both  kinds  ? 

Harry  had  a  dozen  oranges,  but  he  gave  away 
ten.     How  many  had  he  left  ? 

A  watch  dealer  had  3  dozen  gold  watches  the 
week  before  Christmas  ;  the  day  after  Christmas 
he  had  1  dozen  left.  How  many  dozen  had  he 
sold  ?     How  many  watches  had  he  left  ? 


52  LESSON  12. 

Oral  and  slate  exercises  : 

CROWS. 

9  +  3  -  10  +  2  - 

9  +  8  -=  10  +  ?  = 
9  +  4-10+  ?  = 
9  +  6  =  10+  ?- 
9  +  6  =  10+  ?  = 
9  +  7-10+  ?  = 
9  +  2  -  10  +  ?  - 
9  +  9  -^  10  +  ?  = 
8  +  3  -^  10  +  ?  = 
8  +  5  -^  10  +  ?  - 
8  +  7  =  10  +  ?  = 
8  +  6  -  10  +  ?  = 
8  +  4  =  10+  ?  = 
8  +  8  =  10  +  ?  = 
8  +  9  =  10  +  ?  = 
7  +  5  =  10  +  ?  = 

Note.  When  the  sum  of  the  ones  is  more  than  ten,  we  proceed 
as  follows  :  Suppose  we  have  to  add  7  to  8.  Call  upon  one  of  the 
children  to  put  8  nails  in  the  top  row  of  the  counting-board,  and  7 
in  the  second  row,  and  then  ask.  How  many  nails  are  there  in  the  top 
row  ?  How  many  holes  are  left  ?  How  many  nails  must  we  put  in 
the  top  row  to  make  ten  ?  Let  him  take  2  nails  from  the  7  in  the  sec- 
ond row  and  put  in  the  holes  left  in  the  top  row.  How  many  nails 
now  in  the  top  row  ?  How  many  in  the  second  row  ?  Then  8  and  7 
are  10  and  5,  or  15. 

Continue  this  practice,  a  few  minutes  at  a  time,  until  the  children 
can  dispense  with  the  counting-board  ;  then  continue  it  with  the  inter- 
mediate step  until  they  can  dispense  with  that  step,  and  name  instantly 
the  sum  of  any  two  numbers  that  are  each  less  than  ten. 

'i'his  method  may  seem  tedious,  but  it  is  the  only  method  that  gives 
complete  mastery  of  addition. 


L2. 

ROBINS. 

7  +  7  -  10  +  4  = 

14 

? 

7  +  4  =  10+  ?  = 

? 

? 

7  +  8  =  10  +  ?  = 

? 

? 

6  +  6  =  10+  ?  = 

? 

? 

6  +  5  =  10+  ?  = 

? 

? 

6  +  7  =  10+  ?  = 

? 

? 

6  +  9  =  10  +  ?  = 

? 

? 

6  +  8  =  10  +  ?  = 

? 

? 

5  +  9  =  10  +  ?  = 

? 

? 

5  +  7  =  10  +  ?  = 

? 

? 

5  +  8  =  10+  ?  = 

? 

? 

6  +  6  =  10  +  ?  = 

? 

? 

4  +  8  =  10+  ?  = 

? 

? 

4  +  7  =  10  +  ?  = 

? 

? 

4  +  9  =  10  +  ?  = 

? 

? 

3  +  8  =  10  +  ?  = 

? 

LESSON   13. 


53 


Oral  and  slate  exercises 

SPARROWS. 

8  +  6  -  10  +  ?  =  ? 

7  +  4  ==  10  +  ?  =  ? 

5  +  8  =  10  +  ?  =  ? 

8  +  7  =-  10  +  ?  =  ? 

9  +  3  -  10  +  ?  =  ? 
8  +  5  -  10  +  ?  =  ? 

6  +  5  =  10  +  ?  =  ? 
5  +  7  =  10  +  ?  =  ? 

4  +  9  =  10  +  ?  =  ? 

5  +  8  =  10  +  ?  =  ? 

7  +  6  =  10  +  ?  =  ? 
7  +  9  =  10  +  ?  =  ? 


KINGBIRDS. 


4  +  7  =  10  +  ?  =  ? 

8  +  4  =  10  +  ?  =  ? 

7  +  8  =  10  +  ?  =  ? 

2  +  9  =  10  +  ?  =  ? 

9  +  4  =  10+?  =  ? 
9  +  9  =  10  +  ?  =  ? 

8  +  8  =  10  +  ?  =  ? 

7  +  7  =  10  +  ?  =  ? 
6  +  6  =  10  +  ?  =  ? 

8  +  9  =  10  +  ?  =  ? 

3  +  9  =  10  +  ?  =  ? 
2  +  9  =  10  +  ?  =  ? 


9  +  9  =  ? 

9  +  7  =  ? 
9  +  4  =  ? 
9  +  2  =  ? 
9  +  6  =  ? 
9  +  3  =  ? 
9  +  5  =  ? 
9  +  8  =  ? 
8  +  3  =  ? 
8  +  5  =  ? 
8  +  4  =  ? 
8  +  7  =  ? 
8  +  6  =  ? 


8  +  9^? 
8  +  8  =  ? 
7  +  3  =  ? 
7  +  7  =  ? 
7  +  5  =  ? 
7  +  8  =  ? 
7  +  6  =  ? 
7  +  4  =  ? 
7  +  9  =  ? 
6  +  6  =  ? 
6  +  9  =  ? 
6  +  7  =  ? 
6  +  5  =  ? 


CHICKENS. 

6  +  8  =  ? 

6  +  4  =  ? 

5  +  5  =  ? 

5  +  8  =  ? 

5  +  6  =  ? 

5+7  =  ? 

5+9  =  ? 

4  +  7  =  ? 

4  +  9  =  ? 

4  +  8  =  ? 

3  +  8  =  ? 

3  +  9  =  ? 

2  +  9  =  ? 


54  LESSON   14, 

How  many  days  are  1  week  and  4  days  ?  1  week 
and  5  days  ?    1  week  and  6  days  ?   2  weeks  ? 

John  has  9  cents,  and  Mary  4  cents.  How  many 
have  both  ?     How  many  are  9  and  4  ?   4  and  9  ? 

If  one  lamp  is  worth  6  dollars,  and  another  5 
dollars,  how  much  are  both  worth  ? 

If  there  are  8  boys  in  one  class,  and  5  in  another, 
how  many  are  there  in  both  classes  ? 

If  there  are  6  boys  in  one  class,  and  7  in  another, 
how  many  are  there  in  both  classes  ? 

A  farmer  sold  6  sheep  to  one  man,  and  8  to  an- 
other.    How  many  sheep  did  he  sell  ? 

A  farmer  has  9  cows  in  one  pasture,  and  5  in 
another.  How  many  cows  has  he  in  the  two  past- 
ures ?     How  many  are  9  and  5  ?    5  and  9  ? 

Tom  has  two  hens,  one  white,  and  the  other 
black.  The  white  hen  has  9  chickens,  and  the 
black  hen  has  8  chickens.  How  many  chickens 
have  both  hens  ?    How  many  are  9  and  8  ?  8  and  9? 

James  saw  9  crows  on  the  ground,  and  7  more 
flying  about.     How  many  crows  did  he  see  ? 

There  are  8  blocks  in  one  pile,  and  8  in  another 
pile.     How  many  blocks  are  there  in  both  piles  ? 

Tliere  were  9  chickens  roosting  on  one  pole,  and 
6  on  another  pole.  How  many  chickens  were  roost- 
ing on  both  poles  ?     How  many  are  9  and  6  ? 

If  Harry  paid  8  cents  for  his  block  of  paper,  and 
Ernest  paid  7  cents  for  his,  how  many  cents  did 
the  two  blocks  cost  ? 


LESSON  15.  65 

Oral  and  slate  exercises  : 

CHAIRS.  BOXES. 

-  2  -  10  -  1  =-  9.  13   7  -^  10  -  4  -  6. 
3  -  10  -  ?  -=  ?  13  -  8  =  10  -  ?  =  ? 

-  4  =  10  -  ?  =  ?  13  -  5  =  10  -  ?  =  ? 

-  5  -  10  -  ?  -  ?  14  -  6  -  10  -  ?  -  ? 

-  6  -  10  -  ?  -  ?  14  -  6  -  10  -  ?  =  ? 

-  7  -^  10  -  ?  =  ?  14  -  7  =  10  -  ?  -  ? 
-8-10-?-?  14 -8  =  10-?=? 

-  9  -  10  -  ?  -  ?  14  -  9  =  10  -  ?  =  ? 


1 

12   3  -  10  -  ?  -  ?  15  -  6  -  10  -  ?  =  ? 

12  -  4  -  10  -  ?  -  ?  15  -  7  =  10  -  ?  =  ? 

12  -  5  -  10  -  ?  -  ?  15  -  8  =  10  -  ?  =  ? 

12  -  6  -  10  -  ?  -  ?  15  -  9  =  10  -  ?  -  ? 

12  -  7  -  10  -  ?  -  ?  16  -  7  =  10  -  ?  =  ? 

12  -  8  =  10  -  ?  ==  ?  16  -  8  =  10  -  ?  -  ? 

12  -  9  -  10  -  ?  --  ?  16  -  9  -=  10  -  ?  -^  ? 

13  -  4  =  10  -  ?  -  ?  17  -  8  -  10  -  ?  =  ? 
13  -  5  =  10  -  ?  -  ?  17  -  9  -  10  -  ?  =  ? 
13  -  6  -  10  -  ?  =  ?  18  -  9  -  10  -  ?  =  ? 

Note.  In  Subtraction,  the  pupils  may  use  the  knowledge  acquired 
in  Addition.  Thus,  if  8  is  to  be  subtracted  from  15,  the  answer  sought 
is  obtained  by  discovering  the  number  that  must  be  added  to  8  to 
make  15.  But  it  is  better  to  keep  Subtraction  distinct  from  Addition, 
and  at  this  stage  to  take  two  steps,  just  as  we  did  in  Addition. 

Suppose  we  are  required  to  take  8  from  15.  Let  one  of  the  children 
put  10  nails  in  the  top  row  of  holes  in  the  counting-board,  and  5  in  the 
next  row  below.  We  now  ask  the  following  questions :  How  many 
nails  must  we  take  away  to  leave  10  ?  How  many  more  than  5  are 
we  required  to  take  away  ?  And  3  nails  from  10  nails  leave  ?  Then 
15-8  =  10-3  =  7. 


56 


LESSON  16. 

Oral  and  slate 

exercises  : 

BUTTONS. 

NEEDLES. 

PINS. 

12  -  3  - 

14-8  = 

11-6 

13  -  6  - 

12-6  = 

15-7 

11-5  = 

11-3  = 

13-4 

15  -  9  = 

16-8  = 

13-7 

16-7  = 

13-9  = 

12-5 

13-8  = 

15-8  = 

11-8 

11-7  = 

17-9  = 

14-7 

12-9  = 

11-2  = 

12-8 

15-6  = 

12-7  = 

16-9 

14-6  = 

14-5  = 

18-9 

11-4  = 

12-4  = 

13-5 

11-9  = 

16-8  = 

14-9 

If  you  pay  17  dollars  for  a  table,  and  8  dollars 
for  a  chair,  how  many  dollars  more  do  you  pay  for 
the  table  than  for  the  chair  ? 

John  has  16  marbles,  and  James  has  9.  How 
many  more  has  John  than  James  ? 

Take  1  week  from  14  days.  How  many  days 
are  left  ?     How  many  weeks  are  left  ? 

I  have  17  miles  to  walk.  After  I  have  walked 
9  miles,  how  many  more  have  I  to  walk  ? 

A  milkman  has  16  cows.  If  he  sells  7,  how 
many  will  be  left  ? 

A  farmer  had  16  turkeys,  but  a  fox  carried  off 
8  of  them.     How  many  were  left  for  the  farmer  ? 


LESSON   17.  67 

Alice  has  15  chickens.  If  6  are  black,  and  the 
rest  are  white,  how  many  are  white  ? 

If  Ernest  had  9  marbles  more,  he  would  have  15. 
How  many  marbles  has  he  ? 

The  first  train  in  the  morning  had  7  cars,  and 
the  second  train  had  15  cars.  How  many  more 
cars  did  the  second  train  have  than  the  first  train  ? 

Mary  picked  15  quarts  of  blueberries,  and  George 
picked  8  quarts.  How  many  more  quarts  did  Mary 
pick  than  George  ? 

George  caught  14  trout,  and  his  brother  caught 
8  trout.  How  many  more  did  George  catch  than 
his  brother  ? 

Henry  had  14  cents,  but  spent  6  cents  for  lem- 
ons.    How  many  cents  had  he  left  ? 

Miriam  is  14  years  old.  How  old  was  she  7 
years  ago  ?    9  years  ago  ? 

Lucy's  father  and  mother  together  gave  her  14 
cents.  Her  father  gave  her  9  cents.  How  many 
cents  did  her  mother  give  her  ? 

There  were  14  rolls  on  the  table  before  break- 
fast, and  only  5  after  breakfast.  How  many  rolls 
were  eaten  at  breakfast  ? 

Frank  had  13  cents.  He  had  one  five-cent  piece, 
and  the  rest  one-cent  pieces.  How  many  one-cent 
pieces  did  he  have  ? 

Mary's  mother  had  13  eggs.  She  used  4  for  a 
pudding.     How  many  were  left  ? 

How  many  are  14  minus  6  ?    15  minus  8  ? 


^^  LESSON   18. 

I  sent  by  mail  two  books,  and  paid  13  cents 
postage.  The  postage  for  one  was  8  cents.  How 
much  was  the  postage  for  the  other  ? 

A  farmer  had  13  lambs.  How  many  had  he  left 
if  he  sold  6  ?   if  he  sold  7  ? 

Tom  had  13  oranges,  but  he  gave  away  9.  How 
many  had  he  left? 

Edna's  class  numbers  12.  If  5  are  boys,  how 
many  are  girls  ? 

Harry  had  12  papers  to  sell.  After  he  had  sold 
9,  how  many  had  he  to  sell  ? 

Lucy  had  12  plums,  and  Alice  had  4.  How 
many  more  had  Lucy  than  Alice  ? 

In  two  pods  there  were  12  peas.  If  there  were 
6  in  one  pod,  how  many  were  there  in  the  other  ? 

Erwin  found  a  nest  of  12  eggs.  If  he  carried  3 
of  the  eggs  into  the  house,  how  many  were  left  ? 

Fred  had  12  cents.  How  many  had  he  left  if 
he  spent  8  cents  ?   if  he  spent  7  cents  ? 

Jane  bought  11  yards  of  ribbon,  and  used  6  yards. 
How  many  yards  had  she  left  ? 

Lucy  is  11  years  old,  and  Mary  7.  How  many 
years  older  is  Lucy  than  Mary  ? 

Frank  bought  3  oranges  for  9  cents,  and  sold 
them  for  11  cents.     How  many  cents  did  he  gain  ? 

Grace  had  11  cents,  and  paid  5  cents  for  car-fare. 
How  many  cents  had  she  left  ? 

There  were  11  saucers  on  the  table,  but  3  had 
no  cups.     How  many  had  cups  ? 


LESSON   19. 


TWELVK.     12. 

(o)  (ft) 


iiii     III 


Look  at  the  number  picture  marked  (a). 
How  many  dots  are  there  in  each  row  ? 
How  many  rows  are  there  ? 
How  many  dots  in  the  three  rows  ? 
Then  how  many  are  3  times  4  dots  ? 

A  line  of  dots  running  up  and  down  the  page  is  called  a  column. 

How  many  dots  in  each  column  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  four  columns  ? 

Then  how  many  are  4  times  3  dots  ? 

How  many  3's  in  12  ?     How  many  4's  in  12  ? 

Look  at  the  number  picture  marked  (b). 

How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  two  rows  ? 

Then  how  many  are  2  times  6  dots  ? 

How  many  dots  are  there  in  each  column  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  six  columns  ? 

Then  how  many  are  6  times  2  dots  ? 

How  many  2's  in  12  ?     How  many  6's  in  12  ? 

Find  i  of  12  ;   i  of  12  ;   i  of  12  ;   *  of  12. 
12^2  =  ?        12^3  =  ?        12^4  =  ?        12^6-? 
2x3  =  ?  2x4  =  ?  2x5  =  ?  2x6  =  ? 

3x3  =  ?  3x4  =  ?  4x3  =  ?  6x2  =  ? 


60  LESSON   20. 

THE  FOOT-RULE  AND  THE  YARD-STICK. 

Measure  the  yard-stick  with  the  foot-rule.  How 
many  feet  long  is  the  yard-stick  ? 

A  carpet  is  a  yard  wide.  How  many  feet  wide 
is  the  carpet  ? 

How  many  yards  in  3  feet  ?  in  6  feet  ?  in  9  feet  ? 
in  12  feet  ? 

How  many  feet  in  2  yards  ?  in  3  yards  ?  in  4 
yards  ?   in  i  of  a  yard  ? 

If  the  distance  between  two  windows  is  3  yards, 
how  many  feet  is  the  distance  ? 

Your  foot-rule  is  marked  off  into  12  divisions. 
What  is  each  division  called  ?  How  many  inches, 
then,  make  a  foot  ? 

How  many  inches  in  ^  a  foot  ?  i  of  a  foot  ?  i  of 
a  foot  ?    f  of  a  foot  ?    I  of  a  foot  ? 

What  part  of  a  foot  are  6  inches  ?  4  inches  ? 

How  many  more  inches  are  10  inches  than  6 
inches  ?  than  5  inches  ?  than  3  inches  ?  than 
7  inches  ?   than  2  inches  ? 

Remember :   12  inches  make  1  foot. 
3  feet      make  1  yard. 

If  there  are  8  yards  of  wall-paper  in  a  roll,  how 
many  yards  are  there  in  i  of  a  roll  ? 

If  it  takes  2  yards  of  ribbon  to  trim  a  hat,  how 
many  yards  will  it  take  to  trim  6  hats  ? 

Edna's  mother  had  8  yards  of  velvet.  She  used 
i  of  her  velvet.     How  many  yards  were  left  ? 


LESSON  21.  61 

Measure  with  the  foot  rule :" 

1.  The  length  of  a  page  of  your  reader. 

2.  The  length  of  the  top  of  your  desk. 

3.  The  length  of  a  pane  of  glass  in  the  window. 

4.  The  width  of  a  pane  of  glass  in  the  window. 

5.  The  length  of  your  slate. 

6.  The  width  of  your  slate. 

7.  The  length  of  the  face  of  the  blackboard. 

8.  The  width  of  the  face  of  the  blackboard. 

9.  The  length  of  a  page  of  your  copybook. 

Measure  with  the  yard  stick : 

10.  The  width  of  the  floor  of  this  room. 

11.  The  length  of  the  floor  of  this  room. 

Draw  on  the  board  a  line  12  inches  long,  as 
nearly  as  you  can  without  measuring.  Measure 
this  line,  and  tell  me  how  long  it  really  is. 

Draw  a  line  6  inches  long,  as  nearly  as  you  can. 
Measure  the  line,  and  tell  me  how  long  it  really  is. 

Draw  a  square,  one  inch  on  each  side. 

Draw  a  square  with  its  sides  2  inches  long,  and 
divide  it  into  four  smaller  squares. 

How  many  square  inches  in  a  square,  the  sides 
of  which  are  2  inches  long  ? 

How  many  square  inches  in  a  square,  the  sides 
of  which  are  3  inches  long  ? 

Draw  a  square  with  its  sides  3  inches  long,  and 
divide  it  into  nine  smaller  squares. 

Note.   The  Teacher  should  give  exercises  in  measuring  daily. 


62 


LESSON   22. 


FOURTEEN.     14. 

(a)  (6) 


I 


•  • 


Look  at  the  number  picture  marked  (a). 

How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  two  rows  together  ? 

How  many  dots,  then,  are  2  times  7  dots  ? 

How  many  cokimns  are  there  of  2  dots  each  ? 

How  many  dots  in  the  seven  columns  ? 

How  many  dots,  then,  are  7  times  2  dots  ? 

If  you  divide  14  dots  into  two  equal  numbers, 
how  many  will  there  be  in  each  number  ? 

14^2  =  ?      iofl4--?      2x7-?      7x2  =  ? 

Count  by  2's  to  14.     How  many  7's  in  14  ? 

How  many  skates  are  7  pairs  of  skates  ? 

Alice  has  7  two-cent  pieces.  How  many  apples 
at  one  cent  each  can  she  buy  ? 

How  many  weeks  do  1 4  days  make  ? 


2x2-? 

2x5  =  ? 

4^2  =  ? 

10-^5  =  ? 

2x3  =  ? 

2x6  =  ? 

6-^3  =  ? 

12  ^  2  =  ? 

2x4  =  ? 

2x7  =  ? 

8^2  =  ? 

14^7-? 

8  +  4  =  ? 

6  +  5  =  ? 

9  +  5  =  ? 

8  +  9  =  ? 

9  +  6  =  ? 

7  +  6  =  ? 

5  +  7  =  ? 

8  +  5  =  ? 

7  +  8  =  ? 

9  +  4  =  ? 

6  +  9  =  ? 

7  +  9  =  ? 

14  ~  8  =  ? 

17-8  =  ? 

14  -  5  =  ? 

16  -  7  =  ? 

15-7  =  ? 

14-9  =  ? 

13-6  =  ? 

13 -7-? 

16-9  =  ? 

13  -  5  =  ? 

12-7  =  ? 

18  -  9  =  ? 

LESSON   23.  63 

FIFTEEN.     16. 

(a)  (b) 


•  •  • 


Look  at  the  number  picture  marked  (a). 

How  many  dots  are  there  in  each  row  ? 

How  many  rows  of  dots  are  there  ? 

How  many  dots  in  the  three  rows  ? 

How  many  dots,  then,  are  3  times  5  dots  ? 

How  many  dots  are  there  in  each  cohimn  of  dots  ? 

How  many  columns  of  dots  are  there  ? 

How  many  dots  in  the  five  columns  ? 

How  many  dots,  then,  are  5  times  3  dots  ? 

Look  at  the  number  picture  marked  (h). 

How  many  sets  of  5  each  in  15  ? 

Count  by  3's  to  15.     Count  by  5's  to  15. 

15^5  =  ?     15^3-?     •iofl5--?    iofl5-? 

If  one  orange  cost  3  cents,  how  many  cents  will 
5  oranges  cost  ?   will  4  oranges  cost  ? 

How  many  pencils  at  a  cent  each  can  you  buy 
with  3  five-cent  pieces  ?  with  2  five-cent  pieces  ? 

Find  i  of  15  oranges  ;  i  of  15  oranges. 

Emily  has  15  cents  in  five-cent  pieces.  How 
many  five-cent  pieces  has  she  ? 

How  many  feet  long  is  a  string  that  is  5  yards 
long  ?   4  yards  long  ?   3  yards  long  ?   2  yards  long? 

What  part  of  15  pears  are  5  pears  ?   3  pears  ? 

How  many  inches  are  there  in  1  foot  and  i  of  a 
foot  ?   in  1  foot  and  e  of  a  foot  ? 


64  LESSON  24. 


SIXTEEN.     16. 

(a)  (6) 

•  •      •      • 

•  •      •      • 

•  •      •      • 

•  •      •      • 


I 


Look  at  the  number  picture  marked  (a). 

How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  four  rows  ? 

How  many  dots,  then,  are  4  times  4  dots  ? 

Look  at  the  number  picture  marked  (b). 
How  many  dots  are  there  in  each  row  ? 
How  many  rows  are  there  ? 
How  many  dots  in  the  two  rows  ? 
How  many  dots,  then,  are  2  times  8  dots  ? 
How  many  columns  of  2  dots  each  are  there  ? 
How  many  dots  in  the  eight  columns  ? 
How  many  dots,  then,  are  8  times  2  dots  ? 
Count  by  2's  to  16.     Count  by  4's  to  16. 


How  many  2's  in  16  ? 

How  many  4's  in  16  ? 

4x4  =  ?        2x  8-^? 

8x2  =  ?       16^4  =  ? 

16^2-?       16^8  =  ? 

15^3  =  ?       15^5  =  ? 

i  of  16  =  ?       *  of  16  =  ? 

i  of  16  =  ?      i  of  15  =  ? 

At  4  cents  a  quart,  how  many  quarts  of  milk 
can  you  buy  for  16  cents  ? 

At  2  cents  a  pint,  how  many  pints  of  milk  can 
you  buy  for  16  cents  ? 

At  8  cents  a  quart,  how  many  quarts  of  berries 
can  you  buy  for  1 6  cents  ? 


LESSON   25.  66 

OUNCES  IN  A  POUND. 


How  many  ounces  make  a  pound  ? 
It  takes  16  ounces  to  make  1  pound. 

How  many  ounces  in  ^  of  a  pound  ? 

How  many  ounces  in  i  of  a  pound  ? 

What  part  of  a  pound  are  8  ounces  ? 

What  part  of  a  pound  are  4  ounces  ? 

How  many  ounces  in  a  quarter  of  a  pound  of  tea  ? 

How  many  ounces  in  a  half  of  a  pound  of  tea  ? 

What  will  a  pound  of  prunes  cost,  if  half  of  a 
pound  costs  8  cents  ? 

What  will  a  pound  of  raisins  cost,  if  a  quarter 
of  a  pound  costs  4  cents  ? 

If  I  buy  three-quarters  of  a  pound  of  candy,  how 
many  ounces  of  candy  do  I  buy  ? 

How  many  4-ounce  weights  are  equal  to  a  pound 
weight  ?  How  many  8-ounce  weights  ?  How  many 
2-ounce  weights  ?     How  many  1-ounce  weights  ? 

What  part  of  a  pound  are  2  ounces  ?  4  ounces  ? 

How  many  1-ounce  weights  are  equal  to  a  2-ounce 
weight  ?   a  4-ounce  weight  ?   an  8-ounce  weight  ? 

If  1  egg  weighs  2  ounces,  how  many  eggs  will  it 
take  to  weigh  a  pound  ?   a  half-pound  ? 


66  LESSON   26. 

EIGHTEEN.     18. 

(a)  (6) 


I 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  three  rows  ? 

How  many  dots,  then,  are  3  times  6  dots  ? 

How  many  cohimns  of  dots  are  there  ? 

How  many  dots  in  each  column  ? 

How  many  dots  in  the  six  cokimns  ? 

How  many  dots,  then,  are  6  times  3  dots  ? 

How  many  6's  in  18  ?     How  many  3's  in  18  ? 

Look  at  the  dots  marked  (b). 
How  many  dots  in  the  top  row  ?    in  the  bottom 
row  ?   in  the  two  row^s  ? 

How  many  dots,  then,  are  2  times  9  dots  ? 
How  many  columns  of  2  dots  each  are  there  ? 
How  many  dots,  then,  are  9  times  2  dots  ? 
How  many  2's  in  18  ?     How  many  9's  in  18  ? 
Count  by  2's  to  18.    2+2+2  +  2+2  +  2  +  2+2  +  2. 
Count  by  3's  to  18.     3  +  3  +  3  +  3  +  3  +  3. 
Count  by  6's  to  18.     6  +  6  +  6. 


2x4-? 

2x5  =  ? 

2x6  =  ? 

2x7  =  ? 

2x8==? 

2x9  =  ? 

18^2  =  ? 

18-^3  =  ? 

18^6--? 

18^9  =  ? 

9  +  9  =  ? 

18-9  =  ? 

^ofl8  =  ? 

^ofl8=? 

*  of  18  =  ? 

iof  18  =  ? 

What  part 

of  18  is  9  ? 

What  part 

of  18  is  6  ? 

What  part 

of  18  is  3  ? 

What  part 

of  18  is  2  ? 

LESSON   27.  67 

TWENTY.    20. 

(a)  (b) 


How  many  dots  in  each  row  of  dots  marked  (a)? 

How  many  rows  are  there  ? 

How  many  dots  in  the  four  rows  ? 

How  many  dots,  then,  are  4  times  5  dots  ? 

How  many  columns  of  dots  are  there  ? 

How  many  dots  in  each  cohnnn  ? 

How  many  dots  in  the  five  columns  ? 

How  many  dots,  then,  are  5  times  4  dots  ? 

How  many  5's  in  20  ?     How  many  4's  in  20  ? 

Count  by  4's  to  20.     Count  by  5's  to  20. 

Look  at  the  number  picture  marked  (b). 

How  many  dots  in  the  top  row  ? 

How  many  dots  in  the  bottom  row  ? 

How  many  dots  in  the  two  rows  ? 

How  many  dots,  then,  are  2  times  1 0  dots  ? 

How  many  columns  of  2  dots  each  are  there  ? 

How  many  dots  in  the  10  cohimns  ? 

How  many  dots,  then,  are  10  times  2  dots  ? 

How  many  lO's  in  20  ?     How  many  2's  in  20  ? 

4x5-=?       5x4  =  ?       2x10  =  ?       10x2  =  ? 
20^4  =  ?     20^5  =  ?     20^    2  =  ?       20^10  =  ? 

Count  by  2's  to  19,  beginning  1,  3,  5,  etc. 
Count  by  3's  to  19,  beginning  1,  4,  7,  etc. 
Count  by  3's  to  20,  beginning  2,  5,  8,  etc. 


68  LESSON   28. 

ADDITION    TABLE. 


1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

5 

5 

5 

5 

6 

5 

5 

5 

5 

5 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

7 

7 

7 

7 

7 

7 

7 

7 

7 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Note.  The  Teacher  should  copy  this  addition  table  on  the  board, 
and  require  each  pupil  in  turn  to  name  the  sums  as  she  touches  the 
examples  at  random  with  a  pointer.  She  should  continue  the  drill 
daily  until  every  pupil  is  absolutely  certain  of  the  required  answer. 


LESSON   29.  69 

James  had  2  peaches,  and  Tom  had  5  peaches. 
How  many  did  they  have  together  ? 

Harry  bought  a  quart  of  peanuts  for  6  cents, 
and  a  lead  pencil  for  2  cents.  How  much  money 
did  he  spend  ? 

There  are  7  apples  on  one  limb,  and  2  apples  on 
another.     How  many  apples  on  both  limbs  ? 

Susie  has  8  white  roses,  and  Alice  has  2  red 
roses.     How  many  roses  have  they  together  ? 

Nine  boys  are  at  play,  and  2  boys  are  looking 
on.     How  many  boys  in  all  ? 

John  had  10  marbles,  and  found  2  more.  How 
many  had  he  then  ? 

Mary  had  7  cherries,  and  her  brother  gave  her  3 
more.     How  many  had  she  then  ? 

Alice  had  8  white  chickens,  and  3  brown  chick- 
ens.    How  many  chickens  had  she  in  all  ? 

A  farmer  sold  9  bushels  of  corn  at  one  time,  and 
3  bushels  at  another  time.  How  many  bushels 
did  he  sell  in  all  ? 

Harry  saw  5  birds  sitting  on  a  fence,  and  4  birds 
on  the  ground.     How  many  birds  did  he  see  ? 

Nora  bought  a  quart  of  peanuts  for  6  cents,  and 
an  orange  for  4  cents.  How  much  money  did  she 
spend  ? 

A  boy  paid  3  cents  for  an  orange,  and  8  cents 
for  some  bananas.     How  much  did  he  pay  in  all  ? 

The  cook  used  6  eggs  for  a  pudding,  and  7  eggs 
for  cake.     How  many  eggs  did  she  use  ? 


70  LESSON   30. 

Kate  bought  half  a  quire  of  note  paper  for  6 
cents,  and  a  bunch  of  envelopes  for  5  cents.  How 
much  did  she  pay  for  the  paper  and  envelopes  ? 

Ernest  found  7  eggs  in  one  nest,  and  4  eggs  in 
another  nest.     How  many  eggs  did  he  find  in  all  ? 

Emma  picked  8  quarts  of  berries,  and  Frank 
4  quarts.     How  many  quarts  did  they  both  pick  ? 

There  are  9  apples  in  one  dish,  and  4  apples  in 
another.     How  many  apples  are  there  in  all  ? 

A  farmer  had  9  red  cows,  and  5  red  and  white 
cows.     How  many  cows  had  he  ? 

A  boy  rode  8  miles,  and  walked  5  miles.  How 
many  miles  did  he  go  ? 

A  man  paid  7  dollars  for  a  ton  of  coal,  and  5 
dollars  for  a  cord  of  wood.  How  many  dollars 
did  he  pay  for  the  coal  and  wood  together  ? 

A  man  worked  6  days  one  week,  and  5  days  the 
next  week.     How  many  days  did  he  work  in  all  ? 

School  begins  at  9  o'clock  in  the  morning,  and 
continues  3  hours.  What  o'clock  is  it  when  school 
is  dismissed  ? 

John  had  6  cents,  and  earned  6  cents  more. 
How  much  money  had  he  then  ? 

Jane  paid  9  cents  for  a  slate,  and  4  cents  for 
some  paper.  How  much  did  the  slate  and  paper 
together  cost  ? 

Olive  paid  5  cents  for  a  spool  of  silk,  and  9 
cents  for  two  yards  of  ribbon.  How  much  did  she 
pay  in  all  ? 


LESSON   31.  71 

A  farmer  sold  7  lambs  at  one  time,  and  6  lambs 
at  another  time.     How  many  lambs  did  he  sell  ? 

A  milkman  has  8  Dutch  cows,  and  6  Durham 
cows.     How  many  cows  has  he  ? 

James  paid  9  dollars  for  a  coat,  and  6  dollars 
for  a  vest.     How  much  did  he  pay  for  both  ? 

In  a  school  one  class  has  9  girls,  and  another 
has  7  girls.    How  many  girls  have  the  two  classes  ? 

Harry  caught  8  trout,  and  Tom  caught  7  trout. 
How  many  did  they  catch  in  all  ? 

There  are  8  yards  of  ribbon  in  one  roll,  and  9 
yards  in  another.  How  many  yards  are  there  in 
the  two  rolls  ? 

In  a  game  of  baseball  9  persons  play  on  one 
side,  and  9  persons  on  the  other  side.  How  many 
persons  does  it  take  to  play  the  game  ? 

If  a  boy  buys  an  orange  for  4  cents,  a  pear  for 
3  cents,  and  an  apple  for  2  cents,  how  much  does 
he  pay  for  all  ? 

Alice  bought  a  postage  stamp  for  5  cents,  another 
for  4  cents,  and  another  for  3  cents.  How  much 
did  she  pay  for  the  three  stamps  ? 

A  5-cent  piece,  a  2-cent  piece,  and  9  single  cents 
are  equal  to  how  many  cents  ? 

Tom  paid  3  cents  for  a  top,  2  cents  for  a  ball, 
and  7  cents  for  a  book.     How  much  did  he  pay  ? 

James  hoed  4  rows  of  potatoes,  George  hoed  5 
rows,  and  Oscar  hoed  6  rows.  How  many  rows 
did  they  all  hoe  ? 


72  LESSON  32. 

There  are  7  pies  on  one  shelf,  and  9  pies  on 
another  shelf.  How  many  pies  are  there  on  the 
two  shelves  ? 

There  are  6  eggs  in  one  nest,  4  in  another,  and 
3  in  another.  How  many  eggs  are  there  in  the 
three  nests  together  ? 

Nora  paid  9  cents  for  ribbon,  5  cents  for  buttons, 
and  3  cents  for  pins.  How  much  did  she  pay  for 
all? 

A  lady  bought  a  dress  for  9  dollars,  a  hat  for  4 
dollars,  and  a  parasol  for  3  dollars.  How  much 
did  she  pay  for  all  ? 

If  a  table  is  8  feet  long  and  5  feet  wide,  what  is 
the  number  of  feet  in  one  side  and  the  two  ends  ? 

Harry  had  7  five-cent  pieces,  4  two-cent  pieces, 
and  8  one-cent  pieces.  How  many  pieces  of  money 
had  he  in  all  ? 

Alice  picked  6  quarts  of  berries,  Kate  6  quarts, 
and  Florence  5  quarts.  How  many  quarts  did 
they  all  pick  together  ? 

In  a  certain  garden  there  are  6  pear  trees,  7 
peach  trees,  and  5  cherry  trees.  How  many  trees 
are  there  in  the  garden  ? 

James  picked  7  boxes  of  strawberries  on  Monday, 
3  boxes  on  Tuesday,  and  6  boxes  on  Wednesday. 
How  many  boxes  did  he  pick  ? 

Frank  bought  a  pencil  for  4  cents,  a  penholder 
for  3  cents,  and  a  block  of  paper  for  9  cents. 
How  much  did  he  have  to  pay  for  all  ? 


LESSON   33.  73 
SUBTRACTION    TABLE. 

123456789  10 

1     -1     -1     -1     -1     -1     -1     -1     -1  -1 


2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

-2 

-2 

-2 

-2 

-2 

-2 

-2 

-2 

-1 

-2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

-3 

-3 

-3 

-3 

-3 

-3 

-3 

-3 

-3 

-3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

-4 

-4 

-4 

-4 

-5 

-5 

-5 

-5 

-5 

-5 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

-5 

-5 

-5 

-5 

-5 

-5 

-5 

-5 

-5 

-5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

-6 

-6 

-6 

-6 

-6 

-6 

-6 

-6 

-6 

-6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

-7 

-7 

-7 

-7 

-7 

-7 

-7 

-7 

-7 

-7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

-8 

-8 

-8 

-8 

-8 

-8 

-8 

-8 

-8 

-8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

-9 

-9 

"9 

-9 

-9 

-9 

-9 

-9 

-9 

-9 

10     11      12     13     14     15     16     17     18     19 
10  -10   -10  -10  -10  -10  -10  -10  -10    -10 


Note.  The  Teacher  should  copy  this  substraction  table  on  the 
board,  and  require  each  pupil  in  turn  to  name  the  differences  as  she 
touches  the  examples  at  random  with  a  pointer.  She  should  continue 
the  drill  daily  until  every  pupil  is  absolutely  certain  of  the  required 
answer. 


74  LESSON   34. 

Kobert  had  9  cents,  and  spent  4  of  them  for  an 
orange.     How  many  cents  had  he  left  ? 

From  a  string  14  inches  long,  4  inches  were  cut 
off.     How  many  inches  remained  ? 

A  hen  had  11  chickens.  A  hawk  caught  4  of 
them.     How  many  chickens  were  left  ? 

There  were  13  crows  on  the  groimd.  Four  of 
them  flew  away.     How  many  were  left  ? 

A  baker  sold  10  loaves  of  bread  in  the  morning, 
and  7  loaves  in  the  afternoon.  How  many  more 
loaves  did  he  sell  in  the  morning  than  in  the 
afternoon  ? 

A  farmer  raised  19  barrels  of  apples,  and  sold  9 
barrels  ?     How  many  barrels  had  he  left  ? 

From  a  dozen  cans  of  tomatoes  three  cans  were 
used.     How  many  cans  were  left  ? 

Alice  has  7  dolls.  How  many  more  must  she 
get  in  order  to  have  10  dolls  ? 

Ernest  has  14  ducks  and  6  geese.  How  many 
more  ducks  has  he  than  geese  ? 

Ellen  is  11  years  old,  and  Susan  is  7  years  old. 
How  many  years  older  is  Ellen  than  Susan  ? 

A  carpenter  had  a  board  15  feet  long.  He 
sawed  off  a  piece  7  feet  long.  How  many  feet 
long  was  the  other  piece  ? 

A  farmer  sold  a  calf  for  11  dollars,  and  a  pig 
for  3  dollars.  How  much  more  did  he  receive  for 
the  calf  than  for  the  pig  ?  How  much  did  he 
receive  for  the  calf  and  pig  together  ? 


LESSON   35.  76 

A  milkman  has  13  cows.  Six  of  them  are  dark 
red  cows,  and  the  rest  are  black  and  white.  How 
many  of  them  are  black  and  white  ? 

Robert  has  to  travel  16  miles.  How  many  miles 
remain  after  he  has  gone  7  miles  ? 

How  many  eggs  must  you  put  with  7  eggs  in 
order  to  have  a  dozen  eggs  ? 

There  were  12  rats  in  the  stable,  but  5  of  them 
were  caught  in  a  trap.     How  many  rats  escaped  ? 

In  a  pigeon  house  there  were  16  pigeons,  but  9 
flew  away.     How  many  pigeons  remained  ? 

Mary  hemmed  15  handkerchiefs,  and  Ellen  only 
7.     How  many  more  did  Mary  hem  than  Ellen  ? 

A  farmer  had  17  lambs.  He  sold  8  of  them. 
How  many  lambs  had  he  left  ? 

A  sitting  hen  had  13  eggs  under  her,  but  only 
9  chickens  came  out.  How  many  eggs  had  no 
chickens  ? 

Seventeen  spiders  waited  for  flies,  but  7  spiders 
waited  without  catching  any.  How  many  spiders 
caught  flies  ? 

John  had  13  cents,  and  paid  5  cents  for  car  fare. 
How  many  cents  had  he  left  ? 

George  earned  13  cents,  and  spent  8  cents. 
How  many  cents  had  he  left  ? 

Florence  had  16  pinks.  Eight  were  red,  and 
the  rest  w^ere  white.     How  many  were  white  ? 

Bertha  had  18  chickens.  Nine  were  white,  and 
the  rest  were  black.     How  many  were  black  ? 


76  LESSON   36. 

Peter  raised  13  melons,  and  sold  9  of  them. 
How  many  were  left  ? 

There  were  15  eggs  in  a  nest,  but  9  of  them 
were  carried  into  the  house.    How  many  were  left  ? 

Fourteen  lilies  were  growing  in  a  field,  but  a 
boy  picked  9  of  them.    How  many  lilies  were  left  ? 

Harry  has  earned  9  cents  by  selling  newspapers. 
How  many  more  cents  must  he  earn  in  order  to 
have  16  cents  ? 

Kobert  had  17  rows  of  peas.  He  has  hoed 
9  rows.     How  many  more  rows  has  he  to  hoe  ? 

From  a  dozen  cans  of  j)eaches  9  cans  were  used. 
How  many  cans  were  left  ? 

A  gardener  raised  11  dozen  cabbages,  and  sold 
9  dozen.     How  many  dozen  had  he  left  ? 

A  farmer  had  10  oxen,  but  he  sold  one  pair  of 
them.     How  many  oxen  had  he  left  ? 

A  butter  dealer  had  11  pounds  of  butter,  and 
sold  8  pounds.     How  many  pounds  were  left  ? 

A  tea  merchant  bought  14  chests  of  tea.  When 
he  had  sold  8  chests,  how  many  had  he  left  ? 

From  14  yards  of  cloth  a  merchant  sold  5  yards. 
How  many  yards  were  left  ? 

Richard  had  10  lambs.  He  sold  3  of  his  lambs 
to  one  man,  and  2  to  another  man.  How  many 
lambs  remained  ? 

Florence  had  15  roses.  Three  of  the  roses  were 
yellow,  three  were  white,  and  the  rest  were  red. 
How  many  red  roses  did  she  have  ? 


LESSON   37. 


77 


TENS. 


Illllll 


NINETY     90 


SEVENTY     70 


tlltll 


ONE    HUNDRED     lOO 


What  do  we  call  2  tens  ?  3  tens  ?  4  tens  ?  5 
tens  ?   6  tens  ?   7  tens  ?  8  tens  ?  9  tens  ?   10  tens  ? 

How  many  tens  make  ninety  ?  thirty  ?  one  hun- 
dred ?   seventy  ?   fifty  ?   forty  ?   sixty  ?   eighty  ? 

If  I  pay  6  ten-cent  pieces  for  peaches,  and  3  ten- 
cent  pieces  for  pears,  how  many  cents  do  I  spend  ? 

If  I  have  6  ten-cent  pieces  in  one  pocket,  and  4 
in  another,  how  much  money  have  I  ? 

How  many  tens  are  3  tens  and  4  tens  ?  5  tens 
and  2  tens  ?  4  tens  and  4  tens  ?  5  tens  and  5 
tens? 

How  many  ten-cent  pieces  make  a  dollar  ? 

Twenty  is  sometimes  called  a  score. 

How  many  years  are  2  score  years  ? 

How  old  is  a  man  who  is  4  score  years  old  ? 

How  many  years  are  3  score  and  ten  years  ? 


78 


LESSON   38. 


Copy,  and  write  the  results : 

20    20    50    70    30    60    50 
+50   +60   +30   +20   +40   +30   +40 


70 
+30 

80 
+10 

40 
+40 

50 

+50 

60 
+40 

80 

+20 

90 
+10 

50 
-20 

60 
30 

70 
-10 

80 
-50 

90 
-20 

30 
-20 

50 
-30 

70 

-30 

90 
-70 

80 
40 

70 
-20 

90 
-30 

80 
-60 

40 
-20 

3x20  =  ? 
4x20-? 
3x30  =  ? 
4x10  =  ? 


80 
20 
60 
90 


4  =  ? 

2  =  ? 

3  =  ? 
3  =  ? 


2x  20  =  ? 
5x20  =  ? 
2  X  30  =  ? 
2  X  40  =  ? 


60 

40 

80 

100 


2  =  ? 

4  =  ? 
10  =  ? 
10  =  ? 


5x10  =  ? 

5  X  20  =  ? 

9  X  10  =  ? 

lOx  10  =  ? 

^of40  =  ? 
^  of  60  =  ? 
J  of  80  =  ? 
i  of  50  =  ? 


You  have  already  learned  that  we  write  the  fig- 
ure for  the  number  of  tens  in  the  second  place 
from  the  right.  In  what  place,  counting  from  the 
right,  do  we  write  the  hundreds  of  a  number  ? 

Write  on  the  board  the  number  that  contains 
six  hundreds,  no  tens,  and  five  ones. 

If  you  rub  out  the  0,  what  does  the  number 
become  ? 


LESSON  39.  79 

Two  tens  and  one  make  twenty-one,  21. 
Two  tens  and  two  make  twenty-two,  22. 
Two  tens  and  three  make  twenty-three,  23. 
Two  tens  and  four  make  twenty-four,  24. 
Two  tens  and  five  make  twenty-five,  25. 
Two  tens  and  six  make  twenty-six,  26. 
Two  tens  and  seven  make  twenty- seven,  27. 
Two  tens  and  eight  make  twenty-eight,  28. 
Two  tens  and  nine    make  twenty-nine,     29. 

What  are  the  names  of  the  numbers  made  up  of 

3  tens  and  1  ?  3  tens  and  2  ?  3  tens  and  3  ?  3  tens 
and  4  ?  3  tens  and  5  ?  3  tens  and  6  ?  3  tens  and 
7  ?   3  tens  and  8  ?   3  tens  and  9  ? 

What  are  the  names  of  the  numbers  made  up  of 

4  tens  and  1  ?  4  tens  and  2  ?  4  tens  and  3  ?  4  tens 
and  4  ?   4  tens  and  5  ?   4  tens  and  6  ?   4  tens  and  7  ? 

4  tens  and  8  ?   4  tens  and  9  ? 

What  are  the  names  of  the  numbers  made  up  of 

5  tens  and  1  ?  5  tens  and  2  ?  5  tens  and  3  ?  5  tens 
and  4  ?   5  tens  and  5  ?   5  tens  and  6  ?   5  tens  and  7  ? 

5  tens  and  8  ?    5  tens  and  9  ? 

What  are  the  names  of  the  numbers  made  up  of 

6  tens  and  1  ?  6  tens  and  2  ?  6  tens  and  3  ?  6  tens 
and  4  ?   6  tens  and  5  ?   6  tens  and  6  ?   6  tens  and  7  ? 

6  tens  and  8  ?    6  tens  and  9  ? 

What  are  the  names  of  the  numbers  made  up  of 

7  tens  and  1  ?  7  tens  and  2  ?  7  tens  and  3  ?  7  tens 
and  4  ?    7  tens  and  5  ?    7  tens  and  6  ?    7  tens  and  7  ? 


80  LESSON   40. 

Kead  the  numbers:  78;  79;  81;  82;  83;  84; 
85;  86;  87;  88;  89. 

Read  the  numbers:  91;  92;  93;  94;  95;  96; 
97;  98;  99;  100;  200;  300;  400. 

How  many  more  tens  has  the  number  84  than 
72  ?  63  than  31  ?  55  than  15  ?  42  than  2  ?  95 
than  80  ?   65  than  50  ?   94  than  43  ?    99  than  39  ? 

Copy,  and  complete  : 


18  =  10  +  ? 

26  = 

=  2x10  +  ? 

67- 

=  6x10  +  ? 

14-^10  +  ? 

37  = 

=  3x10  +  ? 

84- 

=  8x10  +  ? 

13  =  10  +  ? 

24- 

=  2x10  +  ? 

85- 

=  8x10  +  ? 

19  =  10  +  ? 

35  = 

=  3x10+? 

89- 

=  8xl0  +  ? 

12  =  10  +  ? 

39  = 

=  3x10  +  ? 

86- 

=  8x10  +  ? 

15  =  10  +  ? 

41- 

=  4x10  +  ? 

88- 

=  8x10  +  ? 

16  =  10  +  ? 

47  = 

-4x10  +  ? 

95- 

=  9x10  +  ? 

17  =  10  +  ? 

43  = 

=  4xl0  +  ? 

97  = 

=  9x10  +  ? 

11  =  10  +  ? 

55  = 

=  5x10  +  ? 

93  = 

9X10  +  ? 

20  =  10  +  ? 

59  = 

=  5x10  +  ? 

96  = 

=  9xl0  +  ? 

50  =  10  +  ? 

51  = 

=  5x10  +  ? 

98  = 

=  9  X  10  +  ? 

70  =  10  +  ? 

52  = 

=  5x10  +  ? 

99  = 

=  9x10  +  ? 

Copy,  and  add : 

5        6        2 
3        3        5 

8        7        9 

9 
2 
4 

7       5 
5       7 
3        4 

2 
5 

7 

4 
6 

6 

6  9 
2  5 
6        4 

7       8       5 
7       2       6 
4        9       6 

4 
3 

5 

5        6 
2        1 

7        4 

3 
3 
4 

5 
6 
5 

4  3 
7  6 
6        8 

LESSON  41.  81 

Copy,  and  add,  adding  the  07ies  first : 

22  31            33            25            18  35 
21            33            11            21            30  11 

23  12            13            11            21  21 
32            23            31             22            20  22 


34 

60 

40 

41 

36 

23 

12 

17 

25 

34 

21 

22 

30 

12 

13 

13 

20 

32 

13 

10 

11 

10 

12 

11 

Copy,  and  subtract,  subtracting  the  ones  first : 

65  87  98  78  63  77 

43        -55        -67        -52        -51        -35 


99 

76 

95 

46 

37 

89 

-44 

-66 

-54 

-22 

-21 

-65 

62 

71 

92 

85 

74 

52 

-40 

-50 

-70 

-30 

-43 

-50 

Copy,  and  multiply,  multiplying  the  07ies  first : 

21  32  13  24  34  42 

2  2  2  2  2  2 


31 

23 

33 

43 

44 

30 

2 

2 

2 

2 

2 

2 

11 

10 

23 

12 

32 

33 

3 

3 

3 

3 

3 

3 

10 

11 

12 

20 

21 

22 

4 

4 

4 

4 

4 

4 

82  LESSON   42. 


TWENTY-ONE.    21. 

(a)  (6) 


II 


•  •  • 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  of  dots  ? 

How  many  dots  in  the  three  rows  together  ? 

How  many  dots,  then,  are  3  times  7  dots  ? 

How  many  dots  in  each  cohimn  of  dots  ? 

How  many  columns  of  dots  ? 

How  many  dots  in  the  seven  columns  ? 

How  many  dots,  then,  are  7  times  3  dots  ? 

How  many  3's  in  21  ? 

Look  at  the  number  picture  marked  (b). 

How  many  7's  in  21  ? 

3x7-=?  21^3  =  ?  iof21-? 

7x3  =  ?  21^-7  =  ?  ^of21-? 

If  a  pair  of  boots  costs  7  dollars,  what  will  3 
pairs  of  boots  cost  ?   2  pairs  of  boots  ? 

If  an  orange  costs  3  cents,  what  will  7  oranges 
cost  ?    6  oranges  ?    5  oranges  ?   4  oranges  ? 

Divide  21  oranges  equally  among  3  boys.  How 
many  oranges  will  each  boy  have  ? 

Divide  21  oranges  equally  among  7  boys.  How 
many  oranges  will  each  boy  have  ? 

There  are  21  apples  in  a  basket,  and  James  takes 
one-third  of  them.    How  many  apples  does  he  take  ? 

If  he  had  taken  t  of  them,  how  many  would  he 
have  taken  ? 


LESSON   43.  83 


TWENTY-FOUR.     24. 

(a)  (h) 


•    ••••••• 


•  ••••• 

•  ••••• 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  of  dots  ? 

How  many  dots  in  the  three  rows  ? 

How  many  dots,  then,  are  3  times  8  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  cohimns  are  there  ? 

How  many  dots  in  the  eight  columns  ? 

How  many  dots,  then,  are  8  times  3  dots  ? 

Look  at  the  dots  marked  (b). 

How  many  dots  in  each  row  ? 

How  many  rows  of  dots  ? 

How  many  dots  in  the  four  rows  ? 

How  many  dots,  then,  are  4  times  6  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  six  columns  ? 

How  many  dots,  then,  are  6  times  4  dots  ? 
3x8  =  ?  8x3-=?  4x6  =  ?  6x4  =  ? 

How  many  3's  in  24  ?     How  many  8's  ?     How 
many  4's  ?     How  many  6's  ? 

24^3  =  ?       24^4  =  ?       24^6  =  ?       24^8  =  ? 
i  of  24  =  ?     i  of  24  =  ?     *  of  24  =  ?     *  of  24  =  ? 

4x2=?     4x3=?     4x4=?     4x5=?     4x6=? 
5x2=?     5x3=?     5x4=?     6x3=?     6x4=? 


84  LESSON  44. 

TWENTY-FIVE.    26. 

(a)  (b) 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  five  rows  ? 

How  many  dots,  then,  are  5  times  5  dots  ? 

How  many  5's  in  25  ?     iof2o  =  ?     25-^5-? 

Count  by  5's  to  25  ?     Count  by  4's  to  24. 

Note.  Assist  the  pupil  by  dots  to  count  by  3's,  4's,  etc.,  but  only 
so  long  as  such  assistance  is  necessary. 

Count  by  3's  to  24.     Count  by  2's  to  24. 

Count  by  6's  to  24.     Count  by  8's  to  24.     ' 

Count  by  3's  to  25,  beginning  1,  4,  etc. 

Count  by  3's  to  23,  beginning  2,  5,  etc. 

Count  by  4's  to  25,  beginning  1,  5,  etc. 

Count  by  4's  to  22,  beginning  2,  6,  etc. 

Count  by  4's  to  23,  beginning  3,  7,  etc. 

There  are  5  plates  in  a  row,  and  each  plate  has 
5  apples  on  it.    How  many  apples  on  the  5  plates  ? 

If  you  divide  25  oranges  equally  among  five  lit- 
tle girls,  how  many  oranges  will  each  girl  have  ? 

If  you  have  25  oranges,  how  many  times  can 
you  give  away  oranges  if  you  give  5  each  time  ? 

How  many  eggs  make  a  dozen  ?   a  half-dozen  ? 

How  many  inches  make  a  foot  ?  How  many 
feet  a  yard  ?     How  many  quarts  a  gallon  ? 


LESSON   45.  85 

TWENTY-SEVEN.    27. 

(«)  (6) 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  three  rows  together  ? 

How  many  dots,  then,  are  3  times  9  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  cohimns  are  there  ? 

How  many  dots  in  the  nine  columns  ? 

How  many  dots,  then,  are  9  times  3  dots  ? 

How  many  3's  in  27  ?     How  many  9's  ? 

27^3-?     lof27-^?     27-9  =  ?     iof27-? 

How  many  three-cent  stamps  can  I  buy  for  27 
cents  ?   for  24  cents  ?   for  21  cents  ? 

In  one  yard  there  are  3  feet.  How  many  feet 
in  9  yards  ?   in  8  yards  ?   in  7  yards  ?   in  6  yards  ? 

At  9  cents  a  quart,  how  much  will  3  quarts  of 
berries  cost  ?     2  quarts  of  berries  ? 


2xl  =  ? 

3x1  =  ? 

4x2  =  ? 

6x2  =  ? 

2x2  =  ? 

3x2  =  ? 

4x3  =  ? 

6x3  =  ? 

2x3-? 

3x3  =  ? 

4x4  =  ? 

6x4  =  ? 

2x4  =  ? 

3x4  =  ? 

4x5  =  ? 

7x2  =  ? 

2x6  =  ? 

3x5  =  ? 

4x6  =  ? 

7x3  =  ? 

2x6  =  ? 

3x6  =  ? 

5x2  =  ? 

8x2  =  ? 

2x7  =  ? 

3x7  =  ? 

5x3  =  ? 

8x3  =  ? 

2x8  =  ? 

3x8=?  " 

5x4  =  ? 

9x2  =  ? 

2x9  =  ? 

3x9  =  ? 

5x5  =  ? 

9x3  =  ? 

86  LESSON   46. 

TWENTY-EIGHT.     28. 

(a)  (6) 


•  •    •    •    • 

•  •    •    •    • 


•    !•{•<• 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  four  rows  together  ? 

How  many  dots,  then,  are  4  times  7  dots  ? 

How  many  dots  in  each  cohimn  ? 

How  many  columns  of  dots  are  there  ? 

How  many  dots  in  the  seven  columns  ? 

How  many  dots,  then,  are  7  times  4  dots  ? 

How  many  4's  in  28  ?     How  many  7's  in  28  ? 

4x7  =  ?       7x4  =  ?      28-^4  =  ?      28-^7  =  ? 

At  4  cents  a  quart,  what  will  6  quarts  of  milk 
cost  ?     What  will  7  quarts  cost  ? 

At  6  cents  a  quart,  what  will  4  quarts  of  berries 
cost  ?     What  will  3  quarts  cost  ? 

At  7  cents  a  quart,  what  will  4  quarts  of  berries 
cost  ?     What  will  3  quarts  cost  ? 

At  7  cents  a  cake,  how  many  cakes  of  maple 
sugar  can  you  buy  for  28  cents  ? 

If  it  takes  4  men  7  days  to  dig  a  certain  ditch, 
how  long  will  it  take  1  man  to  dig  the  ditch  ? 

If  it  takes  a  man  28  days  to  build  a  certain  wall, 
how  many  days  will  it  take  him  to  build  a  quarter 
of  the  wall  ?     Three-quarters  of  the  wall  ? 

What  part  of  28  is  7  ?  What  part  of  24  is  4  ? 
What  part  of  24  is  8  ?     What  part  of  27  is  9  ? 


LESSON   47.  87 

THIRTY.    30. 


(a) 
•      •      •      < 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  are  there  ? 

How  many  dots  hi  the  five  rows  ? 

How  many  dots,  then,  are  5  times  6  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  cohunns  of  dots  are  there  ? 

How  many  dots  in  the  six  columns  ? 

How  many  dots,  then,  are  6  times  5  dots  ? 

How  many  6's  in  30  ?     How  many  5's  in  30  ? 

What  part  of  30  is  6  ?     What  part  of  30  is  5  ? 

5x6-^?      6x5--?      30-^5==?      30^6  =  ? 

How  many  cents  ai'e  6  five-cent  pieces  ? 

How  many  five-cent  stamps  can  you  buy  for  30 
cents  ?   for  25  cents  ?   for  20  cents  ? 

When  berries  are  6  cents  a  quart,  how  many 
quarts  can  you  buy  for  30  cents  ?   for  24  cents  ? 

How  many  more  is  i  of  30  than  ^  of  30  ? 

How  many  tens  in  30  ?  How  many  fives  in  i  of 
30  ?   in  -h  of  30  ?   m  i  of  30  ? 

How  many  sixths  of  30  must  you  take  to  have 
i  of  30  ?   to  have  J  of  30  ? 

How  many  sixths  of  any  number  must  you  take 
to  have  i  of  the  number  ?   to  have  ^  of  the  number  ? 

How  many  inches  in  3  of  a  foot  ?  in  I  of  a  foot  ? 

How  many  inches  in  ^  of  a  foot  ?  in  f  of  a  foot  ? 


88  LESSON   48. 

SLATE    ADDITION. 

Add  8  ones  to  6  tens  and  7  ones. 

Write  the  6  tens  and  7  ones 67 

Then  write  the  8  ones  under  the  7  ones  .  .  .     8 
Add  the  ones.  75 

How  many  are  8  ones  and  7  ones  ?     15. 
How  many  tens  and  how  many  ones  in  15  ? 
Write  the  5  ones  in  the  ones'  place  under  8. 
What  shall  be  done  with  the  1  ten  ? 
Add  it  to  the  6  tens,  and  we  have  7  tens. 
Now  write  the  7  tens  in  the  tens'  place. 
Read  the  answer.  Howmany  tensandonesin  75? 

Add  7  ones  to  2  tens  and  8  ones. 
Add  8  ones  to  2  tens  and  5  ones. 
Add  6  ones  to  3  tens  and  7  ones. 
Add  4  ones  to  4  tens  and  9  ones. 
Add  9  ones  to  4  tens  and  7  ones. 
Add  5  ones  to  5  tens  and  5  ones. 
Add  7  ones  to  7  tens  and  3  ones. 


68 
+8 

76 

+  5 

47 
+  6 

28 
+  4 

35 

+  8 

24 

+  9 

56 

+  4 

57 
+  9 

65 

+  7 

69 

+  4 

63 

+  8 

55 

+  5 

84 

+  7 

87 

+  3 

88 

+  9 

79 

+  6 

88 

+  8 

79 

+  9 

33 

±1 

46 
+  8 

57 
+  7 

64 

+  9 

77 
+  9 

86 
+  9 

LESSON   49.  89 

Add  3  tens  and  7  ones  to  4  tens  and  6  ones. 

Write  the  4  tens  and  6  ones 46 

Then  the  3  tens  and  7  ones 37 

Add  the  ones.  83 

How  many  are  7  ones  and  6  ones  ?     13. 
How  many  tens  and  how  many  ones  in  13  ? 
Write  the  3  ones  in  the  ones'  place  under  the  7. 
What  shall  be  done  with  the  1  ten  in  13  ? 
Add  it  to  the  tens. 

1  ten  and  3  tens  are  ?   and  4  tens  more  ? 
Write  the  8  in  the  tens'  place. 
Therefore  the  sum  of  46  and  37  is  83. 
Add  5  tens  and  3  ones  to  1  ten   and  8  ones. 
Add  7  tens  and  6  ones  to  1  ten    and  5  ones. 
Add  3  tens  and  7  ones  to  3  tens  and  6  ones. 
Add  3  tens  and  3  ones  to  3  tens  and  9  ones. 
Add  2  tens  and  5  ones  to  5  tens  and  5  ones. 
Add  4  tens  and  9  ones  to  4  tens  and  8  ones. 
Add  6  tens  and  4  ones  to  1  ten   and  9  ones. 
Add  3  tens  and  8  ones  to  4  tens  and  7  ones. 


64 
18 

48 
29 

76 
18 

57 
19 

35 
56 

56 
24 

55 
38 

28 
36 

55 
29 

35 
16 

68 
19 

39 
26 

48 
32 

65 
19 

53 

28 

57 
35 

48 
27 

34 

28 

90 

LESSON  50. 

Add: 

67 

74 

57 

29 

39 

59 

19 

16 

38 

34 

47 

38 

36 

19 

32 

17 

23 

18 

14 

46 

28 

23 

19 

57 

20 

18 

47 

27 

30 

35 

14 

36 

15 

22 

17 

17 

17 

23 

18 

25 

49 

24 

34 

49 

56 

38 

28 

18 

16 

24 

26 

27 

34 

57 

12 

15 

16 

27 

39 

19 

25 

23 

39 

47 

39 

35 

28 

28 

14 

22 

23 

39 

27 

35 

27 

17 

26 

14 

38 

19 

38 

39 

26 

25 

28 

57 

25 

12 

19 

37 

35 

18 

28 

14 

17 

14 

16 

18 

29 

38 

45 

26 

18 

19 

25 

34 

39 

19 

27 

24 

36 

24 

12 

45 

27 

37 

56 

17 

19 

28 

28 

19 

12 

19 

29 

38 

35 

25 

22 

44 

39 

18 

LESSON  51.  91 

THIRTY-TWO.    32. 

(a)  (6) 


mil 


A     A   1    A     A 

•  • 

•  • 

•  • 

•  • 

How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  of  dots  ? 

How  many  dots  in  the  4  rows  ? 

How  many  dots,  then,  are  4  times  8  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  columns  of  dots  are  there  ? 

How  many  dots  in  the  eight  columns  ? 

How  many  dots,  then,  are  8  times  4  dots  ? 

4x8-?       8x4-?       32-4  =  ?       32  ^8  =  ? 

How  many  shoes  will  a  blacksmith  need  to  shoe 
8  horses  all  round  ? 

A  teamster  has  32  horses.  How  many  four- 
horse  teams  can  he  form  ?  How  many  eight-horse 
teams  ? 

At  4  cents  a  quart,  how  many  quarts  of  milk 
can  you  buy  for  32  cents  ?   for  28  cents  ? 

At  8  cents  a  pint,  how  many  pints  of  cream  can 
you  buy  for  32  cents  ?   for  24  cents  ? 

Four  weeks  make  a  lunar  month.  How  many 
weeks  are  there  in  8  lunar  months  ?   in  7  ?   in  6  ? 

At  8  cents  a  pound,  how  much  will  4  pounds  of 
sugar  cost  ?    3  pounds  ?   2  pounds  ? 

How  many  pears  in  i  of  32  pears  ?  in  i  of  32 
pears  ?   in  i  of  24  pears  ?   in  f  of  24  pears  ? 


92  LESSON  52. 

THE  PECK. 


QUART. 


Note.  These  wooden  measures  are  used  for  measuring  dry  articles, 
such  as  oats,  wheat,  beans,  potatoes,  etc. 

How  many  pints  in  one  quart  ? 

How  many  quarts  make  one  peck  ?  * 

Eight  quarts  make  one  peck. 

How  many  2-quart  measures  of  oats  will  a  peck 
measure  hold  ?     How  many  4-quart  measures  ? 

One  quart  of  oats  is  what  part  of  a  peck  of  oats  ? 
Two  quarts  of  oats  are  what  part  of  a  peck  ?  four 
quarts  ? 

How  many  quarts  in  2  pecks  ?   in  4  pecks  ? 

If  the  peck  measure  is  half-full  of  beans,  how 
many  more  quarts  of  beans  will  it  hold  ? 

If  the  peck  measure  is  a  quarter-full  of  oats, 
how  many  more  quarts  will  it  hold  ? 

If  the  peck  measure  is  three-quarters  full  of 
cranberries,  how  many  quarts  of  cranberries  are 
in  it  ?     How  many  more  quarts  will  it  hold  ? 

How  many  quarts  in  ^  of  a  peck  ?  in  i  of  a 
peck  ?   in  I  of  a  peck  ? 

At  2  cents  a  quart,  what  will  a  peck  of  corn  cost  ? 

At  3  cents  a  quart,  what  will  a  peck  of  nuts  cost  ? 

At  4  cents  a  quart,  what  will  a  peck  of  peas  cost  ? 

*  Let  the  pupil  discover  the  answer  hy  trial. 


LESSON   53. 
THE  BUSHEL,. 


93 


How  many  pints  make  a  quart  ? 

How  many  quarts  make  a  peck  ? 

How  many  pecks  make  a  bushel  ? 

Four  pecks  make  one  bushel. 

How  many  pecks  in  a  half-bushel  ? 

One  peck  of  corn  is  what  part  of  a  bushel  of  corn  ? 

Two  pecks  are  what  part  of  a  bushel  ?  Three 
pecks  are  what  part  of  a  bushel  ? 

How  many  quarts  in  a  peck  of  berries  ? 

How  many  quarts  in  a  half-bushel  of  berries  ? 

How  many  quarts  in  a  bushel  of  berries  ? 

How  many  quarts  in  three-quarters  of  a  bushel? 

In  24  quarts  how  many  pecks  ? 

In  32  quarts  how  many  pecks  ? 

If  a  bushel  basket  is  half-full  of  apples,  how 
many  more  pecks  of  apples  will  it  hold  ? 

If  a  bushel  basket  is  three-quarters  full  of  apples, 
how  many  more  pecks  of  apples  will  it  hold  ? 

A  bushel  of  oats  weighs  32  pounds.  How  much 
does  a  peck  weigh  ?     How  much  do  4  quarts  weigh  ? 

What  part  of  a  bushel  are  4  quarts  ?    8  quarts  ? 


94 


(«) 


LESSON   54. 
THIRTY-FIVE.    35. 


(&) 


•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

•  •  • 

How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  of  dots  ? 

How  many  dots  in  the  five  rows  ? 

How  many  dots,  then,  are  5  times  7  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  columns  of  dots  ? 

How  many  dots  in  the  seven  columns  ? 

How  many  dots,  then,  are  7  times  5  dots  ? 

How  many  7's  in  35  ?     How  many  5's  in  35? 

5x7  =  ?       7x5  =  ?       35^7  =  ?      35^5  =  ? 

How  many  halves  of  a  number  make  the  entire 
number  ?  How  many  thirds  ?  How  many  fourths  ? 
How  many  fifths  ?  How  many  sixths  ?  How 
many  sevenths  ? 

^  of  12  -  ? 

? 

9 


i  of  10 


i  of  20  =  ? 
i  of  24  =  ? 
i  of  25  =  ? 
?  i  of  35  =  ? 

?  I  of  35  =  ? 

At  seven  dollars  a  cord,  how  many  cords  of  wood 
can  be  bought  for  35  dollars?   for  21  dollars  ? 

At  5  cents  a  ride,  how  many  street-car  rides  can 
be  taken  for  35  cents  ?  for  25  cents  ?  for  15  cents? 


2"  Oi  ±^ 

iof  14 
ioi  16 
iof  18 


4  of  15 
iof  18 
iof  21 
i  of  24 


LESSON   55.  95 

THIRTY-SIX.     36. 

(a)  (6) 


How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  ? 

How  many  dots  in  the  four  rows  ? 

How  many  dots,  then,  are  4  times  9  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  columns  ? 

How  many  dots  in  the  nine  columns  ? 

How  many  dots,  then,  are  9  times  4  dots  ? 

How  many  dots  in  each  row  of  dots  marked  (6)  ? 

How  many  rows  ? 

How  many  dots  in  the  six  rows  ? 

How  many  dots,  then,  are  6  times  6  dots  ? 

4x9^?         9x4-?         6x6  =  ?         36-4  =  ? 
36^9  =  ?       36^6  =  ?       iof36  =  ?         ^of36  =  ? 

How  many  four-cent  stamps  can  I  buy  for  36 
cents  ?   for  28  cents  ?   for  32  cents  ?   for  24  cents? 

At  9  cents  a  yard,  how  many  yards  of  calico 
can  I  buy  for  36  cents  ?  for  18  cents  ?  for  27  cents  ? 

At  6  cents  a  quart,  how  many  quarts  of  milk 
can  I  buy  for  36  cents  ?  for  24  cents  ?  for  30  cents  ? 

4x2  =  ?    4x4  =  ?    4x6  =  ?    4x8  =  ? 
4x3  =  ?    4x5  =  ?    4x7  =  ?    4x9  =  ? 


96 


(a) 


LESSON   56. 
FORTY.    40. 


I 


(&) 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  ? 

How  many  dots  in  the  five  rows  ? 

How  many  dots,  then,  are  5  times  8  dots  ? 

How  many  dots  in  each  column  of  dots  ? 

How  many  columns  ? 

How  many  dots  in  the  eight  columns  ? 

How  many  dots,  then,  are  8  times  5  dots  ? 

How  many  5's  in  40  ?     How  many  8's  in  40  ? 

5x8=-?        8x5  =  ?        40^5  =  ?        40-^8==? 

At  5  dollars  a  barrel,  how  many  barrels  of  flour 
can  you  buy  for  40  dollars  ?   for  35  dollars  ? 

At  8  cents  a  bottle,  how  many  bottles  of  ink  can 
you  buy  for  40  cents  ?   for  32  cents  ? 

If  one  loaf  of  bread  is  worth  5  cents,  how  many 
cents  are  8  loaves  worth  ?   6  loaves  ? 

If  a  melon  is  worth  8  cents,  how  many  cents  are 
5  melons  worth  ?   4  melons  ? 

How  much  will  a  boy  earn  in  9  weeks,  if  he 
earns  4  dollars  a  week  ? 


i  of  20  -  ? 

i  of  16  =  ? 

i  of  16  -  ? 

iof  30==? 

i  of  32  ==  ? 

i  of  32  =  ? 

iof  40-? 

i  of  40  -  ? 

4  of  40  =  ? 

LESSON   57.  97 

SLATE    SUBTRAC.TIOX. 

The  result  obtained  from  subtracting  a  smaller 
number  from  a  larger  is  called  the  remainder  or 
difference.  The  smaller  number  is  called  the  sub- 
trahend ;  and  the  larger  number,  the  minuend. 

From  5  tens  and  3  ones  take  2  tens  and  8  ones. 

Write  the  5  tens  and  3  ones 53 

Write  the  2  tens  and  8  ones  below 28 

Draw  a  line  underneath 25 

We  cannot  take  8  ones  from  3  ones.  We  there- 
fore take  1  of  the  5  tens  and  put  with  the  3  ones. 

Note.  Illustrate  this.  Let  the  pupil  take  a  bundle  of  ten,  and  slip- 
ping off  the  rubber  bands  put  the  ten  ones  with  the  three  ones. 

We  now  have  13  ones,  and  8  ones  from  13  ones 
leave  5  ones.     We  write  the  5  in  the  ones*  place. 

As  we  have  taken  1  ten  from  the  5  tens,  we  have 
only  4  tens  left,  and  2  tens  from  4  tens  leave  2  tens. 

We  write  the  2  in  the  tens'  place,  and  have  for 
the  remainder  2  tens  and  5  ones ;  that  is,  25. 

Note.    The  entire  work  may  be  shown  as  follows : 

63  40  +  13 

28  20+8 

25  20  +    5  =  25. 

The  pupils,  however,  must  be  taught  from  the  first  to  do  the  work 
without  any  change  of  the  figures, 

75     23     33     31     37     86 
-6-4-5-3     -8     ^ 

67     35     37     32     46     82 

-8    -9    -9     -7     -7     -3 


98  LESSON   58. 

Slate  exercises : . 

75  42  33  64  83  92 

-37       -25       -16         -28         -38         -29 


50 

41 

42 

56 

35 

52 

-29 

-24 

-15 

-27 

-26 

-28 

48 

42 

62 

55 

61 

72 

-19 

-29 

-33 

-27 

-37 

-36 

70 

52 

85 

75 

85 

60 

-37 

-39 

-16 

-36 

-28 

-48 

98 

96 

73 

86 

83 

57 

-69 

-27 

-57 

69 

-27 

-18 

74 

67 

85 

91 

80 

61 

-37 

-19 

-38 

-64 

-55  • 

-28 

64 

73 

81 

80 

43 

82 

-45 

-26 

-33 

-43 

-26 

-57 

94 

72 

91 

80 

51 

90 

-18 

-19 

-29 

-37 

-22 

-23 

•87 

95 

93 

90 

73 

83 

-19 

-26 

-38 

-43 

-37 

-35 

LESSON   59.  99 

Out  of  16  eggs  7  were  used  for  cooking.  How 
many  eggs  were  left  ? 

In  a  class  of  14  pupils  there  are  5  boys.  How 
many  girls  are  there  in  the  class  ? 

In  a  class  of  13  pupils  there  are  6  girls.  How 
many  boys  are  there  in  the  class  ? 

Out  of  15  signal  flags,  8  are  white,  and  the  rest 
blue.     How  many  flags  are  blue  ? 

One  package  of  tea  weighs  16  ounces,  and  another 
weighs  8  ounces.  How  many  more  ounces  in  one 
package  than  in  the  other  ? 

How  much  deeper  is  a  well  21  feet  deep  than  a 
well  18  feet  deep  ? 

How  many  more  are  13  ducks  than  9  ducks  ? 

A  man  has  17  miles  to  go.  After  he  has  gone 
9  miles,  how  many  more  has  he  to  go  ? 

From  a  board  16  inches  long,  a  piece  9  inches 
long  was  cut  off.  How  many  inches  long  was  the 
other  piece  ? 

A  farmer  had  13  lambs  and  sold  5  of  them. 
How  many  had  he  left  ? 

In  a  brood  of  14  chickens  6  are  white,  and  the 
rest  brown.     How  many  chickens  are  brown  ? 

There  were  13  crows  on  the  ground.  7  flew 
away.     How  many  were  left  on  the  ground  ? 

What  number  must  you  add  to  9  to  get  12  ? 

What  number  must  you  add  to  3  to  get  11  ? 

What  number  must  you  take  from  11  to  get  5  ? 

What  number  must  you  take  from  14  to  get  8  ? 


100  LESSON   60. 

The  number  259  is  read  two  hundred  ffty-nine, 
and  is  composed  of  2  hundreds,  5  tens,  and  9  ones. 

Read,  and  give  the  number  of  hundreds,  of  tens, 
and  of  ones,  in  the  following  numbers  : 


362 

715 

826 

987 

567 

571 

157 

628 

789 

657 

263 

751 

682 

879 

765 

623 

286 

307 

978 

576 

175 

268 

703 

798 

675 

517 

862 

370 

897 

756 

Write  in  figures  the  following  numbers  : 

One  hundred  twenty-nine.  One  hundred  nine. 

Two  hundred  thirty-six.  Seven  hundred  eight. 

Two  hundred  twenty-four.  Five  hundred  six. 

Two  hundred  twenty-two.  Four  hundred  seven. 

Five  hundred  nineteen.  Three  hundred  five. 

Seven  hundred  thirteen.  Two  hundred  four. 

Six  hundred  eighteen.  Four  hundred  three. 

Nine  hundred  eleven.  Three  hundred  two. 

Three  hundred  twelve.  Four  hundred  one. 

Three  hundred  sixteen.  Four  hundred  ten. 

In  any  number  containing  hundreds,  tens,  and 
ones. 

The  ones  are  called  units  of  the  first  order. 

The  tens  are  called  units  of  the  second  order. 

The  hundreds  are  called  units  of  the  third  order. 

Remember  that  any  standard  by  which  we  count 
or  measure  is  called  a  unit. 


LESSON   61.  >lOlc 

Find  the  sums : 

128      136      215  320      357 

362      204      32Y  267      198 

416      473      296  376      276 


317 

218 

375 

427 

576 

207 

219 

293 

291 

197 

327 

397 

189 

198 

189 

229 

379 

263 

327 

183 

292 

125 

362 

279 

136 

376 

268 

185 

202 

181 

Find  the  remainders  : 

362      416      473      327      355 
128      137      279      158      278 


811 
624 

821 
583 

725 

258 

527 
279 

283 
196 

615 

209 

913 
467 

916 
529 

874 
389 

767 
488 

531      451      937      873      726 
253      184      690      565      339 


657 
567 

765 
576 

675 
386 

897 

798 

703 
370 

862 
218 

517 
175 

726 
528 

904 

208 

703 
307 

102 


LESSON   62. 
FORTY-TWO.     42. 


(a) 
•    ••••• 


(6) 

• 

•  • 

•  • 

•  • 

• 

•  • 

•  • 

•  • 

• 

•  • 

•  • 

•  • 

• 

•  • 

•  • 

•  • 

• 

•  • 

•  • 

• 

•  • 

•  • 

•  • 

How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  ? 

How  many  dots  in  the  six  rows  ? 

Haw  many  dots,  then,  are  6  times  7  dots  ? 

How  many  dots  in  each  cokimn  of  dots  ? 

How  many  columns  ? 

How  many  dots  in  the  seven  columns  ? 

How  many  dots,  then,  are  7  times  6  dots  ? 

How  many  7's  in  42  ?     How  many  6's  in  42  ? 

6x7=-?         7x6  =  ?         42-7-=?         42-6  =  ? 

At  6  cents  a  pound,  what  will  7  pounds  of  sugar 
cost  ?    6  pounds  ?    5  pounds  ?    4  pounds  ? 

At  7  cents  a  quart,  how  many  quarts  of  blue- 
berries can  you  buy  for  42  cents  ? 

At  6  dollars  a  ton,  how  many  tons  of  coal  can 
be  bought  for  42  dollars  ? 

At  7  cents  each,  what  will  6  melons  cost  ? 

Count  by  2's  to  42.     Count  by  3's  to  42. 

Count  by  4's  to  40.     Count  by  5's  to  40. 

Count  by  6's  to  42.     Count  by  7's  to  42. 

How  many  7's  in  28  ?    35  ?   42  ?   21  ?    14  ? 

How  many  6's  in  24  ?   30  ?   36  ?   42  ?   18  ? 

How  many  5's  in  25  ?    30?    35?   40?   20? 


LESSON  63. 


103 


FORTY-FIVE.     46. 


(«) 


(ft) 


•  • 

•  • 

•  • 

•  • 

• 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

•  • 

How  many  dots  in  each  row  of  dots  marked  (a)  ? 

How  many  rows  ? 

How  many  dots  in  the  five  rows  ? 

How  many  dots,  then,  are  5  times  9  dots  ? 

How  many  dots  in  each  cohmm  of  dots  ? 

How  many  cohimns  ? 

How  many  dots  in  the  nine  columns  ? 

How  many  dots,  then,  are  9  times  5  dots  ? 

How  many  9's  in  45  ?     How  many  5's  in  45  ? 

5x9-^?        9x5---?        45^5^?        45-^9  =  ? 

At  5  cents  a  pound,  how  many  pounds  of  sugar 
can  be  bought  for  45  cents  ?   for  40  cents  ? 

At  9  cents  a  pound,  how  many  pounds  of  candy 
can  be  bought  for  45  cents  ?   for  36  cents  ? 

Copy,  and  write  the  answers : 


2x2--? 

3x2  =  ? 

4x2  =  ? 

5x2  =  ? 

2x3  =  ? 

3x3  =  ? 

4x3  =  ? 

5x3  =  ? 

2x4-^? 

3x4  =  ? 

4x4  =  ? 

5x4  =  ? 

2x5  =  ? 

3x5  =  ? 

4x5  =  ? 

5x5=? 

2x6  =  ? 

3x6  =  ? 

4x6  =  ? 

5x6  =  ? 

2x7  =  ? 

3x7  =  ? 

4x7  =  ? 

5x7=? 

2x8  =  ? 

3x8  =  ? 

4x8  =  ? 

5x8=? 

2x9  =  ? 

3x9  =  ? 

4x9  =  ? 

5x9  =  ? 

104 

LESSON  64. 

Copy,  and  write  the  answers 

: 

4- 

-2  =  ? 

6- 

^3  = 

=  ?          8- 

-4  =  ? 

10- 

-5  =  ? 

6- 

-2-? 

9- 

-3  = 

=  ?        12- 

-4-? 

15- 

-5  =  ? 

8- 

-2  =  ? 

12 

-3  = 

=  ?        16- 

-4-? 

20- 

-5  =  ? 

10- 

-2  =  ? 

15- 

-3  = 

-?        20- 

-4-? 

25- 

-5  =  ? 

12- 

-2-? 

18- 

-3  = 

-?        24- 

-4-? 

30- 

-5  =  ? 

14 

-2=-? 

21- 

3^ 

-  ?        28  - 

-4-^? 

35- 

-5==? 

16- 

-2  =  ? 

24 

-3- 

=  ?        32- 

-4  =  ? 

40- 

-5  =  ? 

18- 

-2-^? 

27- 

-3  = 

=  ?        36- 

-4  =  ? 

45- 

-5  =  ? 

20- 

-2  =  ? 

30- 

-3^ 

=  ?        40- 

-4^? 

50- 

-5  =  ? 

Find 

i  of    4. 

iof    6. 

k  of    8. 

i  of  10. 

i  of  12. 

iof    6. 

i  of    9. 

i  of  12. 

i  of  15. 

i  of  18. 

iof    8. 

*  of  12. 

i  of  16. 

i  of  20. 

i  of  24. 

i  of  10. 

i  of  15. 

i  of  20. 

i  of  25. 

i  of  30. 

i  of  12. 

i  of  18. 

i  of  24. 

i  of  30. 

J  of  36. 

h  of  14. 

i  of  21. 

i  of  28. 

i  of  35. 

i  of  42. 

i  of  16. 

i  of  24. 

I  of  32. 

i  of  40. 

1  of  42. 

i  of  18. 

*  of  27. 

i  of  36. 

i  of  45. 

1  of  35. 

h  oi 

E20. 

^  of  3 

0. 

i  of  40. 

i  of  50. 

1 

T 

of  28. 

When  we  multiply  one  number  by  another,  the 
result  is  called  the  product ;  the  number  multiplied 
is  called  the  multiplicand ;  and  the  number  by 
which  we  multiply  is  called  the  multiplier. 

Name  two  numbers  whose  product  is  :  15  ;  12  ; 
18;  24;  21;  32;  28;  25;  35;  45;  42;  27;  20. 

The  product  of  two  equal  numbers  is  called  a 
square  number.     With  16  buttons  make  a  square. 


LESSON  65.  105 

Multiply  234  by  2. 

Write  the  multiplicand 234 

Under  the  ones  write  the  multiplier 2 

Draw  a  line  below.  AfKQ. 

Multiply  in  order  the  ones,  tens,  and  hundreds,  and  write     ^^^ 

the  result  at  each  step  :  Twice  4  ones  are  8  ones,  twice  3  tens  are  6 

tens,  twice  2  hundreds  are  4  hundreds.    The  product,  therefore,  is  468. 


Find  the  products  : 

342    123 

2      2 

243 

2 

334 
2 

321 

2 

424 
2 

123    132 
3      3 

323 
3 

213 
3 

312 
3 

212 
3 

111    112 

4      4 

121 

i 

211 

4 

212 
4 

222 
4 

When  we  divide  one  number  by  another,  the 
result  is  called  the  quotient ;  the  number  divided 
is  called  the  dividend ;  and  the  number  by  which 
we  divide  is  called  the  divisor. 

Divide  648  by  2. 

Write  the  divisor  at  the  left  of  the  dividend  with  a  2)  648 
curved  line  between  them,  and  draw  a  line  underneath.  — ooT 

Divide  in  order  the  hundreds,  tens,  and  ones,  and  write  oZ4: 

the  result  at  each  step  :  2  in  6  hundreds,  3  hundreds  ;  2  in  4  tens, 
2  tens  ;  2  in  8  ones,  4  ones.    The  quotient,  therefore,  is  324. 

Find  the  quotients  : 

2)428         2)684  2)468  2)864  2)248 

3)369         3)639  3)396  3)693  3)936 

3)963         4)444  4)484  4)448  4)i844 


106  LESSON   66 

KOMAN  NUMERALS. 

The  Roman  method  of  writing  numbers  uses 
these  seven  capital  letters : 

I  =  1;  V  =  5;  X=10;  L  =  50  ; 
C  =  100;       D  =  500;       M=1000. 

Other  numbers  are  written  by  putting  two  or 
more  of  these  letters  together. 

A  letter  written  before  another  of  greater  value 
signifies  the  difference  of  the  values  of  the  letters 
used. 

Thus,  IV  =  4;   IX  =  9;   XL  =  40;   XC  =  90. 

A  letter  written  after  another  of  the  same  or 
greater  value  signifies  the  sum  of  the  values  of  the 
letters  used.     Thus, 

VI  =  6;  Xl  =  ll;        LX  =  60;       CX=110; 

II  =  2;  111  =  3;  VII  =  7;      VIII  =  8  ; 
XX  =  20;    XXX  =  30;    LXX  =  70;    CCC  =  300. 

Numbers  from  10  to  20  are  written  : 

11-X  +  I      =XI;  16-X  +  VI      -XVI; 

12-^X  +  II   -XII;  17-X  +  VII   -XVII; 

13  -  X  +  III  -  XIII ;  18  =  X  +  VIII  -  XVIII ; 

14  =  X  +  IV-XIV;  19-X  +  IX    -XIX. 

15-X  +  V   =XV; 

* 

In  like  manner : 
25-XX  +  V    -XXV;     46  -  XL  +  VI -XL VI; 
29  -  XX  +  IX -XXIX;    69-LX  +  IX=LXIX. 


LESSON  67. 

1 

Complete  with  Roman  numerals : 

1  = 

11  =            21 

35  = 

64 

2  = 

12=  -        22 

45  = 

36 

3  = 

13=           23 

55  = 

46 

4  = 

14=           24 

65  = 

77 

5  = 

15  =           25 

75  = 

88 

6  = 

16  =           26 

85  = 

97 

7  = 

17  =           27 

95  = 

39 

8  = 

18  =           28 

34  = 

98 

9  = 

19=           29 

44  = 

89 

10  = 

20=           30 

54  = 

99 

Complete  with  figures  : 

1  = 

XV  = 

XXIX  = 

XCI 

11  = 

XVI  = 

XXX  = 

XCII 

111  = 

XVII  = 

XL  = 

XCIII 

IV- 

XVIII  = 

XLV  = 

XCIV 

V  = 

XIX  = 

LI  = 

XCV 

VI  = 

XX  = 

LII  = 

XCVI 

VII  = 

XXI  = 

L1II  = 

XCVII 

VIII  = 

XXII  = 

LIV  =- 

XCVIII 

IX  = 

XXIII  = 

LV  = 

XCIX 

x  = 

XXIV  = 

LVI  = 

CVIII 

XI  = 

XXV  = 

LVII  = 

CL 

XII  = 

XXVI  = 

LVIII  = 

CCIX 

XIII  = 

XXVII  = 

LIX  = 

CCXX 

XIV  = 

XXVIII  = 

LX  = 

CCXLV 

107 


108 


LESSON   68. 
MEASURE    OF    TIME. 


When  the  smallest  hand  of  the  clock  has  gone 
round  the  little  circle,  a  minute  has  passed. 

The  little  circle  has  60  spaces,  and  the  hand  goes 
over  one  space  every  second.     Hence, 

Sixty  seconds  make  a  minute. 

When  the  longest  hand  of  the  clock  has  gone 
round  the  large  circle,  an  hour  has  passed. 

How  many  spaces  are  marked  on  the  large  circle  ? 

The  longest  hand  goes  over  one  space  every 
minute.     Hence, 

Sixty  minutes  make  an  hour. 

The  letters  I,  II,  etc.,  mark  the  hour  spaces. 

How  many  hours  have  passed  when  the  hour- 
hand  has  gone  entirely  round  the  face  of  the  clock  ? 

The  hour-hand  goes  round  twice  from  sunrise  to 
sunrise.     Hence, 

Twenty-four  hours  make  a  day. 


LESSON   69.  109 

How  many  minutes  in  a  half  of  an  hour  ?  in  a 
quarter  of  an  hour  ?  in  a  third  of  an  hour  ?  in 
three-quarters  of  an  hour  ? 

What  part  of  an  hour  are  30  minutes  ?  15  min- 
utes ?    20  minutes  ?    10  minutes  ?   45  minutes  ? 

How  many  hours  in  a  half  of  a  day  ?  in  a  quar- 
ter of  a  day  ?   in  a  third  of  a  day  ? 

What  time  of  day  is  shown  on  the  clock-face  ? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  reaches  I  ?   II  ?   Ill  ? 

mi?  V?  VI?  VII?  VIII?  IX?  X?  XI?  XII? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  is  one  minute-space 
beyondl?  II?  III?  V?  VI?  VIII?  IX?  X?XI? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  is  two  minute-spaces 
beyond  I?   II?   III?  IIII  ?   VI?   IX?   X?   XI? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  is  three  minute-spaces 
beyond  I  ?   Ill  ?   V  ?   VII  ?   IX  ?   X  ?   XI  ? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  is  four  minute-spaces 
beyond  II  ?  Ill  ?  V  ?  VI  ?  VII  ?  VIII  ?  IX  ?  X  ? 

What  time  of  day  will  be  shown  on  the  clock- 
face  when  the  minute-hand  is  at  XII  and  the  hour- 
hand  at  I  ?  II  ?  Ill  ?  V  ?  VI  ?  VII  ?  VIII  ?  IX  ? 

At  what  letters  does  the  minute-hand  point  at 
half-past  four  ?  at  quarter-past  four  ?  at  quarter 
of  five  ?   at  20  minutes  to  five  ? 


110  LESSON  70. 

If  a  man  works  8  hours  a  day,  what  part  of  the 
day  (24  hours)  does  he  work  ? 

What  part  of  24  hours  are  4  hours  ?  6  hours  ? 
8  hours.  ?    12  hours  ?    2  hours  ? 

If  a  man  can  dig  one-quarter  of  a  certain  ditch 
in  8  hours,  how  many  hours  will  it  take  him  to  dig 
the  whole  ditch  ? 

If  2  men  can  mow  a  certain  field  in  8  days,  how 
many  days  will  it  take  one  man  to  mow  it  ? 

If  one  man  can  mow  a  certain  field  in  24  days, 
how  many  men  will  it  take  to  mow  the  field  in 
6  days  ?   in  4  days  ?   in  8  days  ?   in  3  days  ? 

How  many  minutes  are  there  in  2  hours  ?  in  3 
hours  ?   in  4  hours  ?   in  5  hours  ?   in  6  hours  ? 

How  many  seconds  are  there  in  2  minutes  ?  in 
4  minutes  ?   in  5  minutes  ?   in  6  minutes  ? 

What  part  of  a  minute  are  30  seconds  ?  15  sec- 
onds ?  12  seconds  ?  20  seconds  ?  40  seconds  ?  45 
seconds  ?    50  seconds  ? 

If  a  man  walks  a  mile  in  20  minutes,  how  many 
miles  at  that  rate  will  he  walk  in  an  hour  ? 

If  a  man  walks  a  mile  in  15  minutes,  how  many 
miles  at  that  rate  will  he  walk  in  an  hour  ? 

At  the  rate  of  one  mile  in  10  minutes,  how  many 
miles  will  a  horse  go  in  an  hour  ? 

At  the  rate  of  one  mile  in  6  minutes,  how  many 
miles  will  a  horse  go  in  one  hour  ? 

At  the  rate  of  one  mile  in  2  minutes,  how  many 
miles  will  a  railway  train  go  in  an  hour  ? 


■ 


Part  III. 

LESSON   1. 
FORTY-EIGHT.    48, 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  six  rows  ? 

How  many  dots,  then,  are  6  times  8  dots  ? 

How  many  dots  are  there  in  each  column  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  eight  columns  ? 

How  many  dots,  then,  are  8  times  6  dots  ? 

6x8  =  ?  8x6  =  ?        48 -^8  =  ?        48 -^6  =  ? 

1  of  48  =  ?        1  of  48  =  ?       I  of  48  =  ?       ^  of  48  =  ? 

At  6  dollars  a  ton,  what  will  8  tons  of  coal  cost  ? 
At  8  dollars  apiece,  what  will  6  hats  cost  ? 
If  a  cow  gives  8  quarts  of  milk  a  day,  in  how 
many  days  will  she  give  48  quarts  ? 

Ill 


112 


LESSON   2. 
FORTY-NINE.    49. 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  seven  rows  ? 

How  many  dots,  then,  are  7  times  7  dots  ? 

Count  by  7's  to  49.     Count  by  8's  to  48. 

7x7  =  ?  49  ^7  =  ?  -fof49  =  ?  2x7  =  ? 

'3x7=?  4x7=?  '5x7=?  6x7=? 

7  +  7  =  ?  49-7  =  ?  42-7=?  35-7  =  ? 

28-7  =  ?  21-7  =  ?  14-7  =  ?  7-7  =  ? 

At  7  cents  a  pound,  what  will  7  pounds  of  rice 
cost  ?  6  pounds  ?  5  pounds  ?  4  pounds  ?  3  pounds  ? 

Copy  and  subtract : 


418 
-166 

219 
-184 

607 
-235 

729 
-327 

839 

-ebb 

905 
-461 

806 
-235 

704 
-194 

603 
-162 

502 
-171 

213 
-151 

314 
-182 

415 
-193 

516 
-264 

617 
-255 

526 
-275 

425 
-283 

324 
-193 

635 
-383 

639 
-379 

LESSON   3. 
FIFTY-FOUR.    64. 


113 


How  many  dots  are  there  in  each  row  ? 
How  many  rows  are  there  ? 
How  many  dots  in  the  six  rows  ? 
How  many  dots,  then,  are  6  times  9  dots  ? 
How  many  dots  are  there  in  each  column  ? 
How  many  columns  are  there  ? 
How  many  dots  in  the  nine  columns  ? 
How  many  dots,  then,  are  9  times  6  dots  ? 
Coimt  by  6's  to  54.     Count  by  9's  to  54. 


6x9  =  ? 

9x6  =  ? 

54  ^  6  =  ? 

54  -  9  =  ? 

J  of  54  =  ? 

1  of  54  =  ? 

I  of  54  =  ? 

-J-  of  54  =  ? 

2x6  =  ? 

'6x6  =  ? 

12  H-  6  =  ? 

36  -^  6  =  ? 

3x6  =  ? 

7x6  =  ? 

18  ^  6  =  ? 

42  -5-  6  =  ? 

4x6  =  ? 

8x6  =  ? 

24  -  6  =  ? 

48  ^  6  =  ? 

5x6  =  ? 

9x6  =  ? 

30  -i-  6  =  ? 

54  H-  6  =  ? 

How  many  tens  and  how  many  ones  in  54  ? 

54  _  6  =  ?  48  -  6  =  ?  42  -  6  =  ?  36  -  6  =  ? 
30-6  =  ?  24-6=?  18-6=?  12-6  =  ? 
54  _  9  =  ?        45  _  9  =  ?        36  _  9  _  9        27  -  9  =  ? 

At  6  cents  a  quart,  what  will  9  quarts  of  milk 
cost  ?    8  quarts  ?    7  quarts  ?    6  quarts  ?    4  quarts  ? 

At  9  cents  a  pint,  what  will  6  pints  of  sirup  cost  ? 
5  pints  ?   4  pints  ?    3  pints  ?    2  pints  ? 


114  LESSON  4. 

If  we  divide  25  by  4,  we  have  6  for  the  quotient 
and  1  for  the  remainder. 

The  quotient  and  remainder  may  be  written  as  a 
complete  quotient,  thus,  6i. 

In  this  quotient,  the  part  i  is  written  by  writ- 
ing the  remainder  above  the  divisor  with  a  line 
between  them. 

Divide,  and  write  the  complete  quotient  under 
the  dividend  in  each  case  : 


2)13 

3) 

20 

3)29 

5)21 

6)13 

2)15 

31 

22 

4)21 

5)27 

5)32 

2)17 

^1 

23 

4)23 

5)33 

6)39 

2)19  ' 

3) 

25 

4)33 

5)34 

6)40 

3)19 

3) 

26 

4)35 

5)37 

6)47 

3)17 

3) 

28 

4)^7 

5)44 

6)53 

2)123 

3)123 

4)  124 

6)126 

2)143 

3)153 

4)128 

6)128 

2)167 

3)157 

4)160 

6)186 

2)165 

3)159 

4)166 

6)180 

2)169 

3)  127 

4)168 

6)248 

2)182 

3)128 

4)204 

6)249 

2)184 

3)187 

4)247 

6)306 

2)187 

3)189 

4)289 

6)368 

LESSON   5. 
FIFTY-SIX.     56. 


115 


i  of  56  =  ? 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  seven  rows  ? 

How  many  dots,  then,  are  7  times  8  dots  ? 

How  many  dots  in  each  column  ? 

How  many  cohimns  are  there  ? 

How  many  dots  in  the  eight  columns  ? 

How  many  dots,  then,  are  8  times  7  dots  ? 

7x8  =  ?         8x7  =  ?       56h-7  =  ?        56  ^8 
}  of  56  =  ?       I  of  56  =  ?       ^  of  56  =  ? 

If  I  of  56  is  14,  and  ^  of  56  is  7,  how  many 
eighths  of  56  are  equal  to  i  of  56  ? 

How  many  eighths  of  56  are  equal  to  J  of  56  ? 

Count  by  8's  to  56.     Count  by  7's  to  56. 

If  a  man  works  8  hours  a  day,  how  many  hours 
will  he  work  in  5  days  ?   in  6  days  ?   in  7  days  ? 

What  will  7  yards  of  print  cost,  at  8  cents  a 
yard  ?   at  7  cents  a  yard  ?   at  6  cents  a  yard  ? 

At  8  cents  a  yard,  how  many  yards  of  cambric 
can  be  bought  for  40  cents  ?    for  48  cents  ? 

At  7  dollars  a  ton,  how  many  tons  of  coal  can 
be  bought  for  49  dollars  ?   for  56  dollars  ? 


116 


LESSON   6. 
SIXTY-THREE.     63. 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  seven  rows  ? 

How  many  dots,  then,  are  7  times  9  dots  ? 

How  many  dots  are  there  in  each  cohimn  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  nine  columns  ? 

How  many  dots,  then,  are  9  times  7  dots  ? 

7x9  =  ?  9x7  =  ?        63 -^7  =  ?        63-9  =  ? 

I  of  63  =  ?       -i-of63  =  ?       iof63  =  ?       |  of  63  =  ? 

How  many  ninths  of  63  are  equal  to  i  of  63  ? 

Count  by  7's  to  63.     Count  by  9's  to  63. 

At  9  cents  a  foot,  what  will  7  feet  of  lead  pipe 
cost  ?   6  feet  ?   4  feet  ?   5  feet  ?   3  feet  ? 

How  many  days  are  there  in  9  weeks  ? 

At  7  dollars  a  week,  how  many  weeks'  board 
can  be  had  for  56  dollars  ?   for  63  dollars  ? 

At  9  cents  a  quart,  how  many  quarts  of  cran- 
berries can  be  bought  for  54  cents  ?   for  63  cents  ? 

How  many  quarts  of  oats  in  7  pecks  of  oats  ? 

How  many  dozen  eggs  in  48  eggs  ? 

How  many  gallons  of  milk  in  36  quarts  of  milk  ? 


LESSON  7. 


117 


7  X  2  =  ? 

7x3  =  ? 

7x4  =  ? 

7x5  =  ? 


7x6  =  ? 
7x7  = 
7x8  = 
7x9  = 


14  H-  7  =  ? 
21  ^  7  =  ? 

28  -H  7  =  ? 
35  H-  7  =  ? 


Copy,  and  find  the  products  : 

12  12  11  11  11 

3  4  5  6  7 


42  ^  7  =  ? 
49  +  7  =  ? 
56  -f-  7  =  ? 
63  ^  7  =  ? 


11 

8 


11 

9 


41 
3 

41 
4 

41 
5 

41 

6 

41 

7 

41 

8 

41 

9 

60 
3 

60 
4 

60 
5 

60 
6 

60 

7 

60 

8 

60 
9 

31 
3 

31 
4 

31 
5 

31 
6 

31 

7 

31 

8 

31 

9 

70 
3 

70' 
4 

70 
5 

70 
6 

70 

7 

70 
8 

70 
9 

80 
3 

80 
4 

80 
5 

80 
6 

80 

7 

50 
8 

60 
9 

91 
3 

91 
4 

91 
5 

91 
6 

91 

7 

71 

8 

61 

9 

80 
3 

80 
4 

80 
5 

80 
6 

80 

7 

80 
8 

80 
9 

81 

7 

71 

8 

61 
9 

91 
6 

61 

8 

41 

7 

31 
6 

118  LESSON   8. 

A  fly  has  6  legs.     How  many  legs  have  9  flies  ? 

A  spider  has  8  legs.  How  many  legs  have  7 
spiders  ?   6  spiders  ?   4  spiders  ?   3  spiders  ? 

An  ox  has  8  hoofs.  How  many  hoofs  have  6 
oxen  ?    5  oxen  ?   4  oxen  ?   3  oxen  ? 

A  man  bought  9  cords  of  wood  at  4  dollars  a 
cord,  and  gave  4  ten-dollar  bills  in  payment.  How 
much  change  should  he  receive  ? 

James  had  7  cents,  and  his  father  gave  him  six 
times  as  much.     How  many  cents  had  he  then  ? 

Ernest  has  9  five-cent  pieces  and  3  cents.  How 
much  money  has  he  ? 

What  will  9  sheep  cost,  at  6  dollars  each  ? 

At  7  cents  a  yard,  what  will  9  yards  of  cotton 
cloth  cost  ?     What  will  8  yards  cost  ? 

A  farmer  sold  9  lambs  for  45  dollars.  How 
much  apiece  did  he  get  for  them  ? 

How  many  lengths  of  9  yards  each  can  be  cut 
from  a  piece  of  silk  63  yards  long  ? 

In  a  schoolroom  there  were  63  seats  arranged  in 
7  rows.     How  many  seats  in  each  row  ? 

Find  the  cost  of  a  dozen  peaches  at  3  for  5  cents. 

Find  the  cost  of  a  dozen  pears  at  3  for  4  cents. 

A  bushel  of  oats  weighs  32  pounds.  How  many 
pounds  will  a  peck  weigh  ?   3  pecks  ? 

A  bushel  of  corn  weighs  56  pounds.  How  many 
pounds  will  a  peck  weigh  ?   2  pecks  ? 

At  56  cents  a  peck,  how  much  must  be  paid  for 
a  quart  of  beans  ?  2  quarts  ?  4  quarts  ?    6  quarts  ? 


LESSON   9. 
SIXTY-FOUR.     64. 


119 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  eight  rows  ? 

How  many  dots,  then,  are  8  times  8  dots  ? 

Count  by  8's  to  64. 

8x8  =  ?  64  ^  8  =  ?  I  of  64  =  ? 

A  man  receives  8  dollars  a  week  for  work.  How 
much  does  he  receive  in  8  weeks  ? 

There  are  8  pints  in  a  gallon.  How  many  pints 
are  there  in  8  gallons  ?   in  7  gallons  ? 

When  flour  is  6  dollars  a  barrel,  what  will  8  bar- 
rels cost  ?    9  barrels  ?    7  barrels  ?   4  barrels  ? 

When  blueberries  are  8  cents  a  quart,  what  will 
7  quarts  cost  ?    8  quarts  ?    6  quarts  ?    5  quarts  ? 

At  7  cents  a  quart,  what  will  a  peck  of  beans 
cost  ?  What  will  9  quarts  cost  ?  What  will  6 
quarts  cost  ?     What  will  4  quarts  cost  ? 

If  a  freight  train  averages  8  miles  an  hour,  in 
how  many  hours  will  it  run  64  miles  ?    56  miles  ? 

64-8  =  ?        56-8  =  ?        48-8  =  ?        40-8  =  ? 
32  -  8  =  ?        24  -  8  =  ?        16  -  8  =  ?  8  - 


—  ? 


120 


LESSON   10. 
SEVENTY-TWO.      72. 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  eight  rows  ? 

How  many  dots,  then,  are  8  times  9  dots  ? 

How  many  dots  are  there  in  each  column  ? 

How  many  columns  are  there  ? 

How  many  dots  in  the  nine  columns  ? 

How  many  dots,  then,  are  9  times  8  dots  ? 


9x8  =  ? 
1  of  72  =  ? 


72  -  8  =  ?        72  -.  9  =  ? 


1  of  72  =  ? 


iof  72 


8  X  9  =  ? 
J  of  72  =  ? 

At  8  dollars  apiece,  what  will  be  the  cost  of  9 
calves  ?   7  calves  ?   8  calves  ?   6  calves  ? 

At  9  cents  a  yard,  what  will  be  the  cost  of  8 
yards  of  cambric  ?    7  yards  ?   6  yards  ? 

A  farmer  sold  8  calves  for  72  dollars.  How 
much  did  he  get  apiece  ? 

If  9  yards  of  muslin  cost  72  cents,  what  is  the 
price  of  the  muslin  a  yard  ? 

How  many  9's  in  36  ?  in  54  ?  in  63  ?  in  45  ? 
in  72?  in  27?   in  18? 

How  many  dozen  in  24  ?   in  36  ?   in  48  ?   in  72  ? 


LESSON   11. 

121 

2x8  = 

=? 

6x8  =  ? 

16-^2  =  ? 

48^6=? 

3x8  = 

=  ? 

7x8  =  ? 

24h-3  =  ? 

56^7  =  ? 

4x8  = 

=? 

8x8  =  ? 

32-^4  =  ? 

64^8  =  ? 

5x8  = 

=  ? 

9x8  =  ? 

40-5  =  ? 

72-9  =  ? 

iofl6  = 

_? 

i-of  32  =  ? 

^of  48  =  ? 

^of  64  =  ? 

1  of  16  = 

_? 

|of  32  =  ? 

I  of  48  =  ? 

1  of  64  =  ? 

i  of  24  = 

=  ? 

J  of  40=? 

^of  56  =  ? 

iof72  =  ? 

iof24  = 

=? 

iof  40  =  ? 

jof  56=? 

i  of  72  =  ? 

Add; 

23 

31 

27 

36 

47              75 

35 

49 

33 

67 

51              24 

47 

36 

29 

73 

68              37 

72 

53 

32 

21 

33              22 

36 

67 

76 

89 

98              57 

84 

74 

88 

37 

65              84 

39 

38 

31 

53 

29              37 

46 

21 

19 

27 

37              18 

Find  the  differences 


225 

87 

313 
56 

321 

28 

337 

89 

235 

88 

312 
147 

482 
279 

663 
392 

671 
289 

817 
465 

476 

279 

567 
378 

676 
387 

576 

378 

637 
239 

122  LESSON   12. 

EIGHTY-ONE.     81. 


How  many  dots  are  there  in  each  row  ? 

How  many  rows  are  there  ? 

How  many  dots  in  the  nine  rows  ? 

How  many  dots,  then,  are  9  times  9  dots  ? 

Comit  by  9's  to  81.     9x9  =  ?     81-9  =  ? 

If  it  takes  9  yards  of  cloth  for  a  dress,  how 
many  yards  will  be  required  for  9  dresses  ? 

If  a  family  uses  9  pounds  of  sugar  a  week,  how 
many  weeks  will  81  pounds  last  the  family  ? 

If  it  takes  7  eggs  for  a  cake,  how  many  eggs  will 
be  required  for  9  cakes  ? 

How  many  days  are  there  in  9  weeks  ? 

If  it  takes  9  yards  of  print  for  a  dress,  how 
many  dresses  can  be  made  from  54  yards  ? 

If  you  sleep  8  hours  every  night,  how  many 
hours  will  you  sleep  in  9  nights  ? 


2x9=? 

6x9=? 

18-9=? 

54-9=? 

3x9=? 

7x9=? 

27^9=? 

63-9=? 

4x9=? 

8x9=? 

36-^9=? 

72-9=? 

5x9=? 

9x9=? 

45^9=? 

81^9=? 

LESSON   13. 
MULTIPLICATION  TABLK. 


123 


2 

3 

1 

4 

5 

TIMES 

TIMES 

TIMES 

TIMES 

1  ARE      2 

1  ARE      3 

1  ARE     4 

1  ARE      5 

2  ARE     4 

2  ARE      6 

2  ARE      8 

2  ARE  10 

3  ARE      6 

3  ARE      9 

3  ARE  12 

3  ARE  15 

4  ARE      8 

4  ARE  12 

4  ARE  16 

4  ARE  20 

5  ARE  10 

5  ARE  15 

5  ARE  20 

6  ARE  25 

6  ARE  12 

6  ARE  18 

6  ARE  24 

6  ARE  30 

7  ARE  14 

7  ARE  21 

7  ARE  28 

7  ARE  35 

8  ARE  16 

8  ARE  24 

8  ARE  32 

8  ARE  40 

9  ARE  18 

9  ARE  27 

9  ARE  36 

9  ARE  45 

6 

7 

8 

9 

TIMES 

TIMES 

TIMES 

TIMES 

1  ARE      6 

1  ARE      7 

1  ARE      8 

1  ARE      9 

2  ARE  12 

2  ARE  14 

2  ARE  16 

2  ARE  18 

3  ARE  18 

3  ARE  21 

3  ARE  24 

3  ARE  27 

4  ARE  24 

4  ARE  28 

4  ARE  32 

4  ARE  36 

5  ARE  30 

5  ARE  35 

5  ARE  40 

5  ARE  45 

6  ARE  36 

6  ARE  42 

6  ARE  48 

6  ARE  54 

7  ARE  42 

7  ARE  49 

7  ARE  56 

7  ARE  63 

8  ARE  48 

8  ARE  56 

8  ARE  64 

8  ARE  72 

9  ARE  54 

9  ARE  63 

9  ARE  72 

9  ARE  81 

124  LESSON   14. 

Kobert  bought  2  postage  stamps  at  3  cents 
apiece.     How  much  did  he  pay  for  them  ? 

A  buggy  has  4  wheels.  How  many  wheels  are 
needed  for  2  buggies  ? 

At  5  cents  each,  how  much  will  2  car  tickets 
cost  ? 

At  6  cents  a  quart,  how  much  wdll  2  quarts  of 
peanuts  cost  ? 

At  7  cents  a  pound,  what  will  be  the  cost  of  2 
pounds  of  loaf  sugar  ? 

At  8  cents  a  yard,  what  will  2  yards  of  calico 
cost? 

At  9  cents  a  cake,  what  will  2  cakes  of  soap  cost  ? 

If  a  horse  goes  9  miles  an  hour  for  3  hours,  how 
many  miles  will  he  go  in  all  ? 

A  box  has  eight  corners.  How  many  corners 
have  3  boxes  together  ? 

If  a  pair  of  boots  costs  7  dollars,  how  many 
dollars  will  3  pairs  of  boots  cost  ? 

If  an  orange  costs  3  cents,  how  many  oranges 
can  you  buy  for  21  cents  ?  for  27  cents  ?  for  24 
cents  ?  for  18  cents  ?  for  12  cents  ? 

At  3  cents  apiece,  how  much  will  4  oranges  cost  ? 

If  a  hat  costs  4  dollars,  how  much  will  4  hats 
cost? 

At  5  dollars  a  barrel,  what  will  be  the  cost  of 
4  barrels  of  flour  ? 

At  6  cents  a  quart,  what  will  be  the  cost  of  a 
gallon  of  milk  ? 


LESSON   15.  125 

At  7  cents  apiece,  what  will  be  the  cost  of  4 
yard-sticks  ? 

At  9  dollars  a  barrel,  what  will  be  the  cost  of  4 
barrels  of  brown  sugar  ? 

At  8  dollars  a  load,  what  will  4  loads  of  bricks 
cost  ? 

A  farmer  sold  5  pigs  for  3  dollars  apiece.  How 
much  did  he  get  for  his  pigs  all  together  ? 

A  farmer  sold  6  barrels  of  apples  at  3  dollars  a 
barrel.     How  much  did  the  6  barrels  bring  ? 

If  one  desk  has  8  drawers,  how  many  drawers 
will  5  desks  of  the  same  pattern  have  ? 

How  many  yards  long  is  a  piece  of  cloth  that  is 
24  feet  long  ? 

How  many  pints  of  milk  will  a  two-gallon  can 
hold? 

How  many  quarts  of  oysters  in  6  gallons  of 
oysters  ? 

The  cook  used  2  dozen  eggs  in  making  six  pud- 
dings. How  many  eggs  on  the  average  did  she 
use  for  each  pudding  ? 

At  5  cents  apiece,  how  many  bananas  can  be 
bought  for  30  cents  ? 

At  4  cents  apiece,  how  many  oranges  can  be 
bought  for  24  cents  ?  At  3  cents  apiece,  how 
many  can  be  bought  for  24  cents  ? 

At  6  cents  a  quart,  how  many  quarts  of  berries 
can  you  buy  for  18  cents  ?  for  36  cents  ?  for  30 
cents  ?  for  24  cents  ?  for  42  cents  ?  for  48  cents  ? 


126  LESSON   16. 

If  a  quarter  of  a  pound  of  candy  costs  9  cents, 
what  will  a  pound  cost  ? 

I  have  40  cents  in  5-cent  pieces.  How  many  5- 
cent  pieces  have  I  ? 

At  10  cents  a  quire,  how  many  quires  of  paper 
can  be  bought  for  40  cents  ? 

James  has  50  cents  in  10-cent  pieces.  How 
many  10-cent  pieces  has  he  ? 

If  36  pounds  of  starch  are  put  up  in  4-pound 
packages,  how  many  packages  will  there  be  ? 

John  has  54  cents.  How  many  quarts  of  pea- 
nuts can  he  buy  at  6  cents  a  quart  ? 

Emma  has  54  cents.  How  many  yards  of  ribbon 
can  she  buy  at  9  cents  a  yard  ? 

At  8  cents  a  quart,  what  will  7  quarts  of  berries 
cost? 

At  7  cents  a  yard,  what  will  8  yards  of  cloth 
cost? 

Robert  has  56  cents.  How  many  packages  of 
candy  can  he  buy  if  each  package  is  8  cents  ? 

An  orchard  has  56  trees,  and  there  are  7  equal 
rows.     How  many  trees  in  each  row  ? 

A  certain  schoolroom  has  7  rows  of  desks,  with 
9  desks  in  each  row.  How  many  desks  in  the  7 
rows  ? 

A  man  can  build  9  yards  of  fence  in  a  day. 
How  many  days  will  it  take  him  to  build  63  yards? 

A  dealer  sold  7  plows  for  63  dollars.  What  was 
the  price  of  one  plow  ? 


LESSON   17.  127 

A  man  took  6  eggs  at  a  time  seven  times  from 
a  box  of  eggs.     How  many  eggs  did  he  take  out  ? 

If  a  ton  of  coal  costs  6  dollars,  how  much  will  9 
tons  cost  ? 

If  a  cord  of  oak  wood  is  worth  7  dollars,  how 
much  will  9  cords  cost  ? 

On  a  table  there  are  9  plates,  and  each  plate  has 
9  peaches.     How  many  peaches  are  on  the  table  ? 

If  one  dozen  buttons  cost  8  cents,  how  much 
will  9  dozen  buttons  cost  ? 

Ernest  has  64  buttons.  How  many  rows  of  8 
buttons  each  can  he  make  ? 

If  a  box  of  butter  weighs  7  pounds,  how  much 
will  8  boxes  weigh  ? 

It  takes  6  candles  to  weigh  a  pound.  How 
many  pounds  will  54  candles  weigh  ? 

At  7  dollars  a  pair,  how  many  pairs  of  boots  can 
be  bought  for  56  dollars  ?  for  63  dollars  ? 

If  three  men  together  earn  9  dollars  a  day,  in 
how  many  days  will  they  earn  54  dollars  ? 

If  a  man  earns  8  dollars  a  week,  in  how  many 
weeks  will  he  earn  56  dollars  ? 

There  are  6  working  days  in  a  week.  How 
many  working  days  are  there  in  7  weeks  ? 

If  9  persons  ride  in  a  coach,  how  many  coaches 
will  be  required  to  carry  72  persons  ? 

If  a  man  has  48  horses,  how  many  6-horse  teams 
can  he  form  ? 

How  many  pecks  in  56  quarts  ? 


128  LESSON   18. 

Copy  and  multiply : 


94 
2 

43 
3 

62 
4 

51 
5 

71 

7 

81 

8 

71 
9 

91 

8 

81 

7 

61 
6 

31 
5 

92 
4 

920 
3 

930 

2 

610 

9 

710 
8 

910 

7 

810 
6 

210 
9 

310 

8 

710 

7 

910 
6 

810 
5 

920 
4 

622 
4 

911 
5 

711 

6 

911 

7 

811 

8 

911 
9 

913 
3 

944 

2 

811 
5 

810 

7 

101 

8 

901 

9 

Copy  and  divide : 

2)266  3)273 

7)567  8)648 

3)213  4)484 

5)550  6)546 

7)567  9)549 

6)546  7)721 


4)364 

5)455 

6)546 

9)729 

7)637 

5)405 

2)468 

6)606 

8)808 

9)909 

8)568 

7)777 

4)884 

5)500 

8)568 

8)856 

9)972 

4)836 

LESSON   19.  129 

Count  to  a  number  greater  than  100  : 

By  2's,  beginning  with  1 ;  with  2. 

By  3's,  beginning  with  1 ;  with  2  ;  with  3. 

By  4's,  beginning  with  1 ;  with  2  ;  with  3  ;  with  4. 

By  5's,  beginning  with  1 ;  with  2 ;  with  3 ;  with  4 
with  5. 

By  6's,  beginning  with  1 ;  with  2 ;  with  3 ;  with  4 
with  5  ;  with  6. 

By  7's,  beginning  with  1 ;  with  2 ;  with  3 ;  with  4 
with  5  ;  with  6  ;  with  7. 

By  8's,  beginning  with  1 ;  with  2 ;  with  3 ;  with  4 
with  6 ;  with  6  ;  with  7  ;  with  8. 

By  9's,  beginning  with  1 ;  with  2 ;  with  3 ;  with  4 
with  5  ;  with  6  ;  with  7 ;  with  8  ;  with  9. 

Note.  Practice  the  above  drill- exercise  until  every  pupil  can  go 
through  it  readily. 

In  counting  by  2's,  beginning  with  2,  we  obtain 
2,  4,  6,  8,  10,  12,  14,  16,  18,  20,  etc. 

These  numbers  are  called  even  numbers. 

In  counting  by  2's,  beginning  with  1,  we  obtain 
1,  3,  5,  7,  9,  11,  13,  15,  17,  19,  etc. 

These  numbers  are  called  odd  numbers.' 

With  what  figures  do  even  numbers  end  ? 

With  what  figures  do  odd  numbers  end  ? 

Does  any  even  number  when  divided  by  2  give 
a  remainder  ? 

Which  of  the  following  numbers  are  odd,  and 
which  even  ? 

5,  7,  10,  26,  36,  38,  47,  50,  51,  55. 


130  LESSON   20. 

How  many  ll's  in  22  ?  in  33  ?  in  44  ?  in  55  ? 
in  66?  in  77?  in  88  ?  in  99  ?  in  110?  in  121  ? 
in  132  ? 

How  many  12's  in  24  ?  in  36  ?  in  48  ?  in  60  ? 
in  72  ?  in  84  ?  in  96  ?  in  108  ?  in  120  ?  in  132  ? 
in  144  ? 

How  many  eggs  are  2  dozen  eggs  ?    3  dozen  ? 

4  dozen  ?    5  dozen  ?   6  dozen  ?    7  dozen  ?    8  dozen  ? 

9  dozen?    10  dozen?    11  dozen?    12  dozen? 

2x11=?  7x11=?  2x12=?  7x12=? 

llx    2=?        llx   7=?        12x   2=?        12x   T=  ? 


3x11=? 

8x11=? 

3x12=? 

8x12=? 

llx   3=? 

llx   8=? 

12x   3=? 

12x    8=? 

4x11=? 

9x11=? 

4x12=? 

9x12=? 

llx   4=? 

llx   9=? 

12x   4=? 

12x   9=? 

5x11=? 

10x11=? 

5x12=? 

10x12=? 

llx   5=? 

11x10=? 

12x   5=? 

11x12=? 

6x11=? 

11x11=? 

6x12=? 

12x11=  ? 

llx   6=? 

11x12=? 

12x   6=? 

12x12=? 

At  12  cents  each,  what  is  the  cost  of  11  slates  ? 

At  12  dollars  each,  what  is  the  cost  of  12  coats  ? 

If  a  man  works  9  hours  a  day,  how  many  hours 
will  he  work  in  2  weeks  ?  in  one  week  and  a  half  ? 

Twelve  months  make  a  year. 

How  many  months  in  2  years  ?   in  7  years  ? 

How  many  years  in  36  months  ?  in  96  months  ? 

Thirty-six  inches  make  a  yard. 

How  many  inches  in  1  yard  ?  in  I  of  a  yard  ?  in 
5  of  a  yard  ?  in  §  of  a  yard  ?  in  3  of  a  yard  and 
i  of  a  foot  ?   in  i  of  a  yard  and  h  of  a  foot  ? 


LESSON   21. 

1  SQUARE  FOOT. 


131 


This  square  represents  a  square  foot. 

How  many  inches  long  is  a  side  of  the  square  ? 

How  many  square  inches  are  there  in  the  square  ? 

144  square  inches  make  1  square  foot. 

A  square  the  side  of  which  measures  1  yard  is 
called  a  square  yard. 

If  the  side  of  a  certain  square  is  1  yard  long, 
how  many  feet  long  is  it  ? 

If  you  cut  a  square  yard  of  brown  paper  into 
strips  a  foot  wide,  how  many  strips  will  you  have  ? 

How  many  square  feet  in  each  strip  ? 

How  many  square  feet  in  the  three  strips  ? 

How  many  square  feet,  then,  in  a  square  yard  ? 

9  square  feet  make  1  square  yard. 

How  many  square  inches  in  a  square  4  inches 
on  a  side  ?  6  inches  ?  7  inches  ?  8  inches  ?  9  inches  ? 

How  many  square  feet  in  a  square  2  feet  on  a 
side  ?    3  feet  ?     4  feet  ?    5  feet  ?    6  feet  ?    7  feet  ? 


132  LESSON   22. 

How  many  pecks  in  8  quarts  ?   in  24  quarts  ? 
How  many  pecks  in  16  quarts  ?    in  32  quarts  ? 
How  many  bushels  in  8  pecks  ?   in  12  pecks  ? 
How  many  bushels  in  4  pecks  ?   in  16  pecks  ? 
Add,  and  give  the  answers  in  bushels  : 

5  bu.  3  pks.  3  qts.  3  bii.  2  pks.  6  qts. 

4  2  4  7        3  6 

6  15                          8        17 
8        0  4  6 3  5 

How  many  quarts  in  2  pints  ?   in  6  pints  ? 
How  many  quarts  in  4  pints  ?   in  8  pints  ? 
How  many  gallons  in  8  quarts  ?   in  12  quarts  ? 
Add,  and  give  the  answers  in  gallons  : 

5  gals.  3  qts.  1  pt.  8  gals.  2  qts.  1  pt. 

6  2         1  6  3  0 

7  2         1  9  3  1 

8  3         1  7  3         0 


How  many  feet  in  12  inches  ?  in  24  inches  ?  in 
36  inches  ?   in  48  inches?   in  60  inches  ? 

How  many  yards  in  3  feet  ?  in  6  feet  ?  in  9  feet  ? 
in  12  feet  ?   in  21  feet  ?   in  27  feet  ?   in  36  feet  ? 

Add,  and  give  the  answers  in  yards : 

6  yds.  1  ft.  9  in.  12  yds.  2  ft.  3  in. 
5          2       7  ^ 

7  2       6 
3  2       2 

How  many  square  feet  in  144  square  inches  ? 
How  many  square  yards  in  9  square  feet  ?  in  18 
square  feet  ?  in  27  square  feet  ?  in  36  square  feet  ? 


15 

1 

4 

13 

2 

3 

19 

0 

2 

LESSON   23.  133 

The  coins  of  the  United  States  are  made  of 
gold,  silver,  nickel,  or  bronze. 

The  double-eagle,  the  eagle,  the  half -eagle,  and 
the  quarter-eagle  are  made  of  gold. 

Twenty  dollars  make  a  double-eagle. 

Ten  dollars  make  an  eagle. 

Five  dollars  make  a  half-eagle. 

Two  and  one-half  dollars  make  a  quarter-eagle. 

The  dollar,  the  half-dollar,  the  quarter-dollar,  and 
ten-cent  piece  are  made  of  silver. 
How  many  cents  make  a  dollar  ? 
One  hundred  cents  make  a  dollar. 
How  many  cents  make  a  half-dollar  ? 
How  many  cent«  make  a  quarter-dollar  ? 
A  ten-cent  piece  is  often  called  a  dime. 
How  many  cents  make  a  dime  ? 

The  five-cent  piece  is  made  of  nickel. 
A  five-cent  piece  is  often  called  a  nickel. 
How  many  cents  make  a  nickel  ? 

The  one-cent  piece  is  made  of  bronze. 
A  one-cent  piece  is  often  called  a  penny. 

How  many  dimes  make  a  half-dollar  ? 
How  many  nickels  make  a  quarter-dollar  ? 
How  many  quarter-dollars  make  a  half-dollar  ? 
How  many  nickels  make  a  half-dollar  ? 
How  many  quarter-dollars  make  a  dollar  ? 
How  many  dimes  make  a  dollar  ? 
How  many  nickels  make  a  dollar  ? 


134  LESSON   24. 

The  sign  $  is  called  the  dollar  sign,  and  is  placed 
before  the  figures. 

One  dollar  is  written  $  1,  or  $  1.00. 

Eleven  dollars  and  twenty-five  cents  is  written 
$11.25. 

The  dot  after  the  $  11  in  $  11.25  means  that  the 
two  figures  on  the  right  of  it  stand  for  cents,  and 
the  figures  on  the  left  of  it  stand  for  dollars. 

The  dot  between  the  figures  for  dollars  and  the 
figures  for  cents  is  called  the  decimal  point. 

Read:  $5.03;  $7.27;  $42.56;  $12.23;  $13.67; 
$67.53;  $18.91;  $98.01;  $107.31;  $121.02. 

How  many  places  do  the  cents  occupy? 

The  cents  always  occupy  two  places. 

Write  in  figures : 

Three  dollars  and  five  cents. 

Forty-five  dollars  and  seventy-three  cents. 

Thirty-five  dollars  and  sixty-seven  cents. 

Nineteen  dollars  and  eighteen  cents. 

Eighty-nine  dollars  and  ten  cents. 

One  hundred  five  dollars  and  two  cents. 

One  hundred  seventeen  dollars  and  one  cent. 

One  hundred  three  dollars  and  three  cents. 

One  hundred  nine  dollars  and  five  cents. 

One  hundred  one  dollars  and  one  cent. 

Two  hundred  seventy  dollars  and  nine  cents. 

Two  hundred  dollars  and  eight  cents. 

Three  hundred  dollars  and  twenty-five  cents. 

Two  hundred  dollars  and  fifty  cents. 


LESSON 

25. 

135 

Add: 

$2.03 
3.04 
3.21 
5.51 

$8.12 
7.32 
5.13 
6.41 

$12.12 
13.13 
21.21 
32.32 

$14.05 
11.10 
31.32 
23.50 

$30.03 
20.02 
40.01 
50.50 

$5.43 
1.27 
3.19 

$9.34 

2.18 
6.25 

$8.27 

9.36 

10.19 

$11.17 
25.25 
37.37 

$13.37 
72.26 
87.19 

Subtract 

.  . 

$7.45  $7.89  $8.59  $9.33  $36.55 

-5.03         -4.63  -5.26  -7.29  -28.00 


$9.51  $5.65  $6.41  $6.73  $17.44 

-3.28         -1.27  -2.38  -1.09  -8.36 


Multiply : 

$1.13  $2.24  $5.10  $8.12  $9.08 

3  4  5  6  7 


$11.07        $12.09  $9.07  $7.09  $6.08 

8  9  9  7  8 


Divide : 

$16.08  by  2.  $12.24  by  6.  $56S6  by  8. 

$12.24  by  2.  $24.12  by  6.  $64.08  by  8. 

$18.36  by  3.  $35.35  by  7.  854.54  by  9. 

$24.12  by  4.  $49.42  by  7.  $81.09  by  9. 

$25.05  by  5.  $56.56  by  7.  $63.72  by  9. 


136  LESSON   26. 

Ten  mills  make  1  cent. 

What  part  of  a  cent  is  one  mill?  2  mills? 
3  mills  ?   5  mills  ?    7  mills  ?    10  mills  ? 

Since  1  mill  is  1  tenth  of  a  cent,  how  many 
cents  are  twenty  mills  ?   30  mills  ?    50  mills  ? 

We  write  mills  on  the  right  of  cents. 

Two  dollars  87  cents  and  5  mills  are  written 
$2,875. 

Thirty-seven  cents  and  5  mills  are  written  $  0.375. 

Read:  $3,607;  $5,546;  $18,364;  $0,253. 

Write  in  figures  : 

Seven  dollars  sixty  cents  and  eight  mills. 
Eleven  dollars  seventy-five  cents  and  five  mills. 
Twenty-one  dollars  two  cents  and  two  mills. 
Ninety-nine  cents  and  seven  mills. 

A  ten-cent  piece  is  often  called  a  dime. 

Ten  dimes  make  a  dollar. 

What  part  of  a  dollar  is  1  dime  ?  2  dimes  ? 
3  dimes  ?  4  dimes  ?  5  dimes  ?  6  dimes  ?   10  dimes  ? 

How  many  tenths  of  a  dollar  make  the  dollar  ? 

How  many  tenths  of  a  cent  make  the  cent  ? 

How  many  tenths  of  any  unit  whatever  make  the 
whole  unit  ? 

Tenths  occupy  one  place,  the  first  place  to  the 
right  of  the  decimal  point. 
•  The  number  seven  and  three-tenths  is  written  7.3. 

The  number  6.5  is  read  six  and  five  tenths. 

The  number  0.7  is  read  seven  tenths. 


LESSON   27.  137 

Since  100  cents  make  a  dollar,  1  cent  is  1  hun- 
dredth of  a  dollar. 

How  many  hundredths  of  a  dollar  are  2  cents  ? 
3  cents  ?   5  cents  ?   10  cents  ?  25  cents  ?  50  cents  ? 

How  many  tenths  of  a  dollar  are  10  cents  ? 

How  many  hundredths  of  a  dollar  are  10  cents  ? 

How  many  hundredths,  then,  make  1  tenth  ? 

10  hundredths  make  1  tenth. 
10  tenths  make  1  unit. 

The  number,  three  and  five  hundredths,  is  writ- 
ten, 3.05.  The  number,  two  and  sixty-four  hun- 
dredths, is  written,  2.64. 

Hundredths  always  occupy  two  places. 

Read:  5.08;  7.21;  10.54;  17.27;  65.65;  7.6; 
6.07;  8.9;  8.09;  7.8;  7.08;    90.9;  90.09;  81.81. 

Write  in  figures : 

Five  and  five  tenths. 

Seventy-five  and  eighty-six  hundredths. 

Nine  hundred  one  and  nine  hundredths. 

Seventy-six  and  twenty-five  hundredths. 

Fifty-five  and  fifty  hundredths. 

How  many  hundredths  are  : 

8  hundredths  +  9  hundredths  ? 
14  hundredths  -  5  hundredths  ? 
16  hundredths  -  7  hundredths  ? 

3x4  hundredths  ?  i  of  63  hundredths  ? 

7x8  hundredths  ?  I  of  56  hundredths  ? 

6x9  hundredths  ?  i  of  36  hundredths  ? 


138  LESSON   28. 

The  number  denoted  by  figures  at  the  right  of 
the  decimal  point  is  called  a  decimal  number,  or 
simply  a  decimal. 

In  adding  or  subtracting  numbers  containing 
decimals  loe  j^ut  the  decimal  point  in  the  result 
directly  under  the  column  of  decimal  points  in  the 
give7i  number's. 

Add: 


51.8 
36.2 
47.6 
15.5 

26.7 
37.5 
62.5 
54.7 

36.3 
57.3 
25.6 
47.5 

63.8 
38.6 
32.7 

87.9 

8.15 
2.63 
7.46 
5.51 

7.62 
7.35 
2.65 
4.57 

6.33 
3.57 
5.26 
7.45 

3.68 
6.38 
2.37 

7.89 

8.51 
-2.36 

7.62 
-3.57 

6.33 
-3.75 

8.63 
-6.83 

92.3 
-35.7 

64.7 
-26.5 

62.5 
-45.7 

75.4 
-b5.b 

9.32 
-7.25 

6.74 
-2.65 

2.56 
-1.19 

7.37 

-2.89 

3.77 
-1.98 

81.2 
-36.9 

47.6 
-28.7 

56.2 
-19.5 

LESSON   29.  139 

A  farmer  paid  $160  for  a  horse  and  i  as  niucli 
for  a  cow.     How  much  did  he  pay  for  the  cow  ? 

A  lady  bought  some  blankets  for  $  15  and  some 
silk  for  $25.  She  gave  ten-dollar  bills  in  pay- 
ment.    How  many  bills  did  she  give  ? 

A  boy  bought  a  pair  of  boots  for  $4.25.  He 
gave  a  five-dollar  bill  in  payment.  How  much 
change  did  he  receive  ? 

A  man  earned  in  a  week  $19.50,  and  spent 
$  12.25.     How  much  did  he  save  ? 

James  earned  $6.25,  and  his  brother  gave  him 
enough  to  make  $  10.  How  much  did  his  brother 
give  him  ? 

What  will  9  barrels  of  flour  cost  at  $6.10  a 
barrel  ? 

What  will  8  sheep  cost  at  $6.10  apiece  ? 

What  will  5  hats  cost  at  $3.10  apiece  ? 

A  lady  bought  a  shawl  for  $11.50,  and  a  hat 
for  $  8.  She  gave  a  twenty-dollar  bill  in  payment. 
How  much  change  did  she  receive  ? 

Henry  bought  3  pounds  of  beefsteak  at  23  cents 
a  pound,  and  gave  a  dollar-bill  in  payment.  How 
much  change  did  he  receive  ? 

At  $  0.50  a  pound,  how  many  pounds  of  Jersey 
butter  can  be  bought  for  $2.50  ? 

How  many  pounds  of  coffee  at  $0.30  a  pound 
can  be  bought  for  $  0.90  ? 

At  8  cents  a  pound,  how  many  pounds  of  rice 
can  be  bought  for  $0.56  ? 


140  LESSON   30. 

THE  YEAR. 

How  many  months  make  one  year  ? 

Twelve  months  make  a  year. 

The  names  of  the  months  in  order  are  : 

January,  February,  March,  April,  May,  June, 
July,  August,  September,  October,  November,  De- 
cember. 

The  spring  months  are  March,  April,  May. 

The  summer  months  are  June,  July,  August. 

The  autumn  months  are  September^  October, 
November. 

The  winter  months  are  December,  January,  Feb- 
ruary. 

Spring,  summer,  autumn,  winter,  are  called  the 
four  seasons  of  the  year. 

Thirty  days  have  September,  April,  June,  and 
November. 

Febiniary  has  28  days,  and  in  leap  years  29  days. 

The  other  months  have  31  days  each. 

Three  hundred  sixty-five  days  make  a  year. 

Three  hundred  sixty-six  days  make  a  leap  year. 

When  the  date  of  the  year  can  be  divided  by  4 
without  remainder,  or  in  case  the  date  ends  in  two 
zeros  by  400,  the  year  is  a  leap  year. 

Which  of  these  years  are  leap  years  ?  1800 ; 
1860;  1872;  1890;  1893;  1892;  1900;  2000. 

In  a  common  year,  how  many  days  from  the  be- 
ginning of  the  year  to  February  15  ?  to  March  31  ? 
to  April  7  ?   to  May  1  ?   to  June  14  ?   to  July  20  ? 


LESSON   31.  141 

THOUSANDS. 

The  number,  10  hundred,  is  called  a  thousand. 
A  thousand  is  written  1,000. 
A  thousand  and  one  is  written  1,001. 
Ten  thousand  and  ten  is  written  10,010. 
One  hundred  twenty  thousand  four  hundred  is 
written  120,400. 

How  many  thousands  and  how  many  ones  in 
7,632  ?   50,023  ?   41,701  ?  417,203  ?  500,230  ? 

Write  in  figures  and  read  all  the  numbers  from 
4,002  to  4,020;  from  80,997  to  81,010;  from 
537,091  to  537,102 ;  from  748,987  to  749,000. 

Read:    5,430;   3,072;   1,010  ;  45,320 ;   70,045; 
40,309;    36,008;     113,079;    273,002;    182,012; 
811,200;  100,256;  500,005;  300,023;  608,300. 
Write  in  figures : 

Four  thousand.  Three  thousand  seven. 

Six  thousand  ten.  Five  thousand  fifteen. 

Eight  thousand  three. 
Nine  thousand  seven  hundred. 
Six  thousand  twenty-eight. 
Seventy-four  thousand  six  hundred. 
Fifteen  thousand  five  hundred. 
Sixty-nine  thousand  thirty-two. 
Seventy-three  thousand  five  hundred  forty-six. 
Eight  hundred  thousand  seven  hundred  five. 
Ninety-six  thousand  eight  hundred  fifty-six. 
Two  hundred  fifty  thousand  two  hundred  fifty. 
Two  hundred  five  thousand  two  hundred  five. 


142  LESSON  32. 

MIT^LIONS. 

When  we  write  numbers  which  contain  thousands 
and  ones,  we  generally  leave  a  little  space  after  the 
last  figure  of  the  thousands,  and  put  a  comma  in 
this  space.     Thus,  236  347  is  written  236,347. 

This  comma  divides  the  figures  into  two  periods, 
the  period  of  thousands  and  the  period  of  ones. 

Forty-eight  thousand  and  thirty-six  sheep  is  writ- 
ten, 48,036  sheep.  Here  we  write  48  for  the  word 
forty-eight ;  then  put  a  comma  after  the  8  for  the 
word  thousand  ;  then  0,  as  there  are  no  hundreds, 
and  lastly,  36  for  the  word  thirty-six. 

The  unit  for  the  ones'  period  is  1  sheep. 

The  unit  for  the  thousands'  period  is  1000  sheep. 

The  unit  for  the  next  higher  period  is  a  million. 

A  million  is   1000    thousands,   and   is   written 

1,000,000. 

The  unit  of  any  period  is  equal  to  1000  units  of 
the  next  lower  period. 

Three  hundred  million  two  hundred  forty-six 
thousand  five  hundred  dollars  is  written 

$300,246,500. 

Here  we  put  a  comma  after  the  300  for  the  word 
million,  and  after  the  246  for  the  word  thousand. 

The  left-hand  period  may  have  one,  two,  or  three 
figures,  but  every  other  period  must  have  three  fig- 
ures, one  figure  for  the  hundreds,  one  for  the  tens, 
and  one  figure  for  the  ones,  of  that  period. 


LESSON   33.  143 

How  many  millions,  thousands,  and  ones  in 
50,032,106  ?  41,107,106  ?  500,200,300  ? 

Read  : 

32,027,020  316,106,207 

100,370,200  70,000,035 

275,701,050  170,202,305 

75,017,500  28,028,280 

57,207,005  202,170,503 

10,987,278  111,798,827 

65,371,954  210,007,500 

87,250,520  120,052,250 

54,054,540  540,504,054 

95,720,027  905,059,950 

Write  in  figures : 

Thirty  million,  twenty-seven  thousand,  one  hun- 
dred twenty  dollars  ? 

Two  hundred  seven  million,  seven  hundred 
twenty  thousand,  three  hundred  dollars. 

Ninety-five  million,  fifty-nine  thousand,  one 
hundred  sixty-six  dollars. 

Five  hundred  nine  million,  five  hundred  four 
thousand,  five  hundred  forty  dollars. 

Twenty  million,  two  hundred  twenty  thousand, 
three  hundred  sixty-four  dollars. 

Nineteen  million,  nineteen  thousand,  nine  hun-- 
dred  nineteen  dollars. 

Thirty-seven  million,  three  hundred  thirty-seven 
thousand,  seven  hundred  dollars. 

Two  hundred  twenty  million,  three  hundred 
thirty  thousand,  four  hundred  forty  dollars. 


144  LESSON   34. 

THOUSANDTHS  AND  TEN-THOUSANDTHS. 

If  a  unit  is  divided  into  ten  equal  parts,  each  part 
is  called  a  tenth  of  the  unit ;  if  into  a  hundred  equal 
parts,  each  part  is  called  a  hundredth ;  if  into  a  thou- 
sand equal  parts,  each  part  is  called  a  thousandth  ; 
if  into  ten  thousand  equal  parts,  each  part  is  called 
a  ten- thousandth. 

Note.  The  Teacher  should  use  the  meter  stick  to  show  the  deci- 
mal parts  of  a  unit.  The  decimeters  show  the  tenths,  the  centimeters 
the  hundredths,  and  the  millimeters  the  thousandths,  of  the  meter. 

Tenths  occupy  one  decimal  place 0.1 

Hundredths  occupy  two  decimal  places  ....  0.21 

Thousandths  occupy  three  decimal  places  .     .     .  0.213 

Ten-thousandths  occupy  four  decimal  places  .     .  0.2134 

The  decimal  0.1  is  read  one  tenth  ;  0.21  twenty- 
one  hundredths  ;  0.213  two  hundred  thirteen  thou- 
sandths ;  0.2134  twenty-one  hundred  thirty-four 
ten-thousandths ;  4.4045  is  read  four  and  four 
thousand  forty-five  ten-thousandths. 

Note.  In  reading  a  number,  part  of  which  is  integral  and  part 
decimal,  pronounce  and  at  the  decimal  point  and  omit  it  in  all  other 
places. 

Read:  1.09;  23.023;  50.107;  7.0017;  7.0209; 
5.5055;  2.3785;  15.0015;  6.2567. 

Write  in  figures  :  two  and  five  tenths ;  two  and 
five  hundredths  ;  two  and  five  thousandths ;  two 
and  five  ten-thousandths ;  two  and  twenty-five  hun- 
dredths ;  two  and  twenty-five  thousandths ;  two 
and  twenty-five  ten-thousandths  ;  two  and  two  hun- 
dred twenty-five  thousandths  ;  two  and  two  hundred 
twenty-five  ten-thousandths. 


LESSON  36.  146 

ADDITION. 

To  test  the  correctness  of  the  work  in  addition, 
we  add  in  a  different  order.  The  results  should  be 
the  same.  Thus,  if  we  have  added  from  the  bottom 
to  the  top,  we  add  from  the  top  to  the  bottom. 

1.  2.             3.             4.  5.  6.  7. 

321  615  522  178  312  124  673 

502  143  617  512  723  780  485 

279  687  843  296  677  379  289 


8. 

9. 

10. 

11. 

12. 

13. 

4321 

3214 

5423 

8372 

70.52 

58.23 

2751 

5467 

6543 

543 

53.84 

1.92 

6284 

873 

7654 

7941 

98.72 

64.95 

863 

9124 

6785 

9078 

8.76 

8.67 

Arrange  and  add,  taking  care  to  have  units  of  the 
same  order  stand  in  the  same  column. 

Decimals  are  easily  arranged  by  taking  care  to 
have  the  decimal  points  stand  in  a  vertical  column. 

14.  43,307;  96,812;  60,798;  21,121. 

15.  83,654;  34,747;  58,659;  32,321. 

16.  59.852;  41.664;  68.054;  90.594. 

17.  10.5921;  27.3007;  31.9789;  2.563. 

18.  $5.86;  1561.75;  128.32;  $40.50. 

19.  121,016;  167,404;  84,121;  m^^Q. 

20.  90.0542;  32.8971;  55.674;  348.78. 

21.  64.3372;  6.4337;  0.3723;  100.733. 

22.  0.415;  70.634;  121.5007;  8.3467. 

23.  8.0213;  15.101;  12.0031;  0.2256. 

24.  121.0015;  100.37;  148.561;  1121.505. 

25.  15.86;  $8.78;  $11.89;  $12.58;  $95.37;  $59.88. 


146  LESSON  37. 

SLATE    EXERCISES. 

1.  John  Dix  deposited  in  the  Third  National 
Bank  of  Boston  $  4321,  and  a  week  later  $  13,893. 
How  much  did  he  deposit  in  all  ? 

2.  The  steamer  Majestic  made  on  four  successive 
days  503,  504,  505  and  505  miles.  How  many 
miles  did  she  make  in  the  four  days  together  ? 

3.  In  1890  the  population  of  New  York  was 
1,513,501,  of  Brooklyn  804,377,  and  of  Jersey 
City  162,317.  What  was  the  population  of  these 
three  cities  ? 

4.  In  1890  St.  Louis  had  460,357  inhabitants, 
Boston  had  447,720,  Baltimore  432,095,  and  San 
Francisco  297,990.  How  many  had  these  four 
cities  together  ? 

5.  In  1890  Chicago  had  1,098,576  inhabitants, 
Milwaukee  206,308,  Minneapolis  164,738,  St.  Paul 
133,156.    How  many  had  these  four  cities  together  ? 

6.  In  1890  Philadelphia  had  1,044,894  inhabi- 
tants, Pittsburgh  238,473,  Alleghany  104,967, 
Scranton  83,450.  What  is  the  population  of  the 
four  largest  cities  of  Pennsylvania  ? 

7.  In  1890  Cincinnati  had  296,309,  Cleveland 
261,546,  Buffalo  255,543,  Detroit  205,669.  How 
many  had  these  four  cities  together  ? 

8.  In  1890  Washington  had  228,160,  New 
Orleans  241,995,  Louisville  161,005,  and  Rich- 
mond 80,838.  Find  the  population  of  these  four 
cities  together. 


LESSON  38. 


147 


SUBTRACTION. 

To  test  tlie  correctness  of  the  work  in  subtrac- 
tion, we  add  the  subtraliend  and  the  remainder. 
The  sum  shouhl  be  equal  to  tlie  minuend. 

Subtract  427  from  736. 


Beginning  on  the  right,  subtract  7  from  1(5,  and  write  9 
below. 

Afterwards  subtract  2,  not  from  3,  but  from  2,  and  write 
3^9        0  below.    Then  subtract  4  from  7,  and  write  3  below. 


736 

427 


Subtract  7658  from  9000. 

9000  Subtract  8  from  10,  and  write  2;  then  subtract  5,  not 

7658      from  10,  but  from  9,  and  write  4  ;  again,  subtract  0  from  9, 
TqTq"     and  write  3  ;  then  subtract  7  from  8,  and  write  1. 


Proof.     Add  7658 
1342 

9000 


Proof. 

Add  427 
309 

736 

Subtract 

: 

1. 

873 
169 

6.  3850 
1929 

11.  60570 
48692 


16.  462085 
345396 


2. 

679 

298 

7. 

5435 
1567 

12. 

20729' 
17934 

17. 

701406 
243859 

3. 

700 
177 

8. 

5634 
5284 

13. 

32405 
21657 

18. 

740052 
698253 

4. 

901 
475 

9. 

9005 
6476 

14. 

20604 
11847 

19. 

402701 
317485 

5. 

506 
347 

10. 

3401 
2085 

15. 

60004 
28597 

20. 

400100 
375916 

148  LESSON   39. 

SUBTRACTION   OF  DECIMALS. 

In  the  subtraction  of  decimals,  make  the  number 
of  decimal  places  in  the  minuend  and  subtrahend 
the  same,  annexing  zeros  if  necessary. 

Subtract  25.468  from  62.1253  ;  and  2.1789  from 
7.2. 

OPERATION.  OPERATION. 

52.1253  7.2000 

25.4680  2.1789 


26.6573  5.0211 

Arrange  so  that  the  decimal  point  of  the  subtra- 
hend shall  be  under  that  of  the  minuend,  and 
subtract  : 


1. 

0.85   - 

-0.79. 

16. 

13.2589-10.06. 

2. 

1.76   - 

-0.98. 

17. 

71.1002-52.387. 

3. 

2.729- 

-1.836. 

18. 

11.2487-5.3579. 

4. 

5.482- 

-3.176. 

19. 

10.9041-9.8765. 

5. 

2.354- 

-2.287. 

20. 

17.3258-16.37. 

6. 

3.826- 

-3.719. 

21. 

2.5-0.025. 

7. 

5.902- 

-3.678. 

22. 

75  -0.7575. 

8. 

5.77  - 

-4.888. 

23. 

1.52-1.0024. 

9. 

9.62  - 

-3.765. 

24. 

129.5-96.349. 

10. 

8.42  - 

-5.661. 

25. 

0.157-0.1547. 

11. 

7.23  - 

-6.562. 

26. 

752.8-4.9732. 

12. 

9.02  - 

-7.163. 

.     27. 

819.3-57.687. 

13. 

4.31   - 

-3.425. 

28. 

83.52-64.743. 

14. 

1.27   - 

-1.198. 

29. 

61.98-4.3554. 

15. 

1.46   - 

-o.or,", 

30. 

6.716-0.8725. 

LESSON   40  149 

SLATE  EXERCISES. 

1.  Shakespeare  was  born  in  1564  and  died  in 
1616.     How  many  years  did  he  live  ? 

2.  Milton  was  born  in  1608  and  died  in  1674. 
How  many  years  did  he  live  ? 

3.  Daniel  Webster  died  in  1852  at  the  age  of  70. 
In  what  year  was  he  born  ? 

4.  President  Washington's  first  inaugural  ad- 
dress contained  1300  words.  His  second  inaugural 
address  contained  134  words.  How  many  more 
words  did  the  first  contain  than  the  second  ? 

5.  President  Lincoln's  first  inaugural  address 
contained  3500  words.  His  second  inaugural  ad- 
dress contained  580  words.  How  many  more  words 
did  the  first  contain  than  the  second  ? 

6.  The  population  of  Kansas  City  was  55,585 
in  1880,  and  132,416  in  1890.    Find  the  increase. 

7.  The  population  of  Denver  was  35,629  in 
1880,  and  106,670  in  1890.     Find  the  increase. 

8.  The  population  of  Omaha  was  30,518  in 
1880,  and  139,526  in  1890.     Find  the  increase. 

9.  The  number  of  silk  looms  in  the  United 
States  in  1880  was  8474,  and  in  1890  the  number 
was  22,569.     Find  the  increase. 

10.  There  are  CL  Psalms.  James  has  read 
XCIX.     How  many  more  has  he  to  read  ? 

11.  A  woman  bought  groceries  to  the  amount  of 
1 3.83.  She  gave  a  five-dollar  bill  in  payment. 
How  much  change  should  she  receive  ? 


150 


LESSON  41. 


MULTIPLICATION. 

If  a  product  greater  than  9  is  obtained  in  multi- 
plying, the  figure  for  the  ones  only  is  written,  and 
the  tens  are  added  to  the  following  product. 


Thus,  in  the  problem  in  the  margin  4  x  8  =  32,  we  write 
the  2  ;  then  4x5  tens  =  20  tens,  and  to  the  20  tens  we  add 
the  3  tens  of  the  last  product,  obtaining  23  tens  or  2  hun- 
dreds and  three  tens  ;  we  write  the  3  ;  then  4x3  hundreds 
=  12   hundreds,    and  to  the  12   hundreds  we    add  the  2 

hundreds  of  the  last  product,  obtaining  14  hundreds,  which  we  write. 

The  entire  product  is  therefore  1432. 


358 
4 

1432 


1.  2x3687. 

2.  2x4783. 

3.  3x2879. 

4.  3x3657. 

5.  5x1953. 

6.  5x2849. 

7.  4x3567. 

8.  4x2586. 

9.  5x6852. 

10.  6x1376. 

11.  6x5647. 

12.  6x3124. 

13.  3x8798. 

14.  7x2342. 

15.  8x4323. 

16.  9x5215. 

17.  4x7826. 


SLATE  EXERCISES. 

18.  5x8267. 

19.  6x6754. 

20.  7x7854. 

21.  7x9384. 

22.  8x4337. 

23.  3x9785. 

24.  3x8694. 

25.  7x2334. 

26.  9x1682. 

27.  5x9889. 

28.  4x8977. 

29.  6x9778. 

30.  7x3879. 

31.  9x3355. 

32.  8x6675. 

33.  7x8643. 

34.  9x6854. 


35.  4x29354. 

36.  5x70528. 

37.  6x56713. 

38.  7x31567. 

39.  8x37582. 

40.  9x56014. 

41.  9x34749. 

42.  9x36927. 

43.  9x73186. 

44.  8x25839. 

45.  7x98325. 

46.  8x63578. 

47.  9x67489. 

48.  7x38697. 

49.  9x48769. 

50.  7x57009. 

51.  8x99798. 


LESSON   42.  151 

If  the  multiplier  has  two  or  more  figures : 

We  7n.ultiply  hy  eachfitjure  separately,  taking  care 

to  jyut  the  first  figure  of  each  product  directly  under 

the  figure  of  the  multiplier  used  in  obtaining  it ; 

and  add  the  products.     Thus, 

Proof.     2046 
7235  '       7235 

2046 


10230 

43410  6138 

28940  4092 

14470  14322 


14802810  14802810 

The  multiplicand  and  multiplier  are  called  fac- 
tors of  the  product.  If  either  factor  is  0,  the 
product  is  0.  The  product  of  two  factors  is  not 
changed  if  the  order  of  the  factors  is  changed. 

To  jjrove  multiplication,  we  change  the  order 
of  the  factors,  and  multiply  again.  The  products 
should  be  the  same  in  both  cases. 

Multiply : 


1. 

114  by  32. 

11. 

714  by  48. 

21. 

3159  by  507. 

2. 

112  by  76. 

12. 

578  by  97. 

22. 

3819  by  206. 

3. 

365  by  56. 

13. 

842  by  86. 

23. 

8769  by  517. 

4. 

372  by  23. 

14. 

682  by  69. 

24. 

5731  by  475. 

5. 

283  by  64. 

15. 

792  by  79. 

25. 

8592  by  486. 

6. 

564  by  47. 

16. 

8763  by  407. 

26. 

7069  by  908. 

7. 

259  by  57. 

17. 

8437  by  502. 

27. 

5604  by  609. 

8. 

538  by  38. 

18. 

9872  by  603. 

28. 

6789  by  789. 

9. 

467  by  59. 

19. 

7356  by  805. 

29. 

4769  by  687. 

10. 

736  by  94. 

20. 

5983  by  704. 

30. 

6897  by  976. 

152  LESSON   43. 

If  the  multiplier  is  10,  100,  1000,  etc.,  we  obtain 
the    product  by  annexing  to  the  multiplicand  as 
many  zeros  as  there  are  in  the  multiplier. 
Thus,  100  times  746  is  74,600. 
In  short,  if  one  or  both  factors  end   in   zeros, 
we  multiply  without  regard  to  the  zeros. 

Then  we  annex  to  the  product  as  many  zeros  as 
there  are  at  the  ends  of  the  factors  together.    Thus, 
To  multiply  74,200  by  230,  we  first  multiply  742 
by  23,  and  obtain  17,066.    To  this  number  we  an- 
nex 3  zeros,  and  get  17,066,000  for  the  true  result. 

Multiply  : 


1. 

467   by  10. 

9. 

56000  by  3480. 

2. 

312   by  100. 

10. 

50060  by  7000. 

3. 

587   by  1000. 

11. 

50400  by  2080. 

4. 

6112  by  3000. 

12. 

47000  by  2070. 

5. 

7281  by  4000. 

13. 

504304  by  100. 

6. 

8127  by  5000. 

14. 

7120   by  7002. 

7. 

43070  by  2000. 

15. 

102039  by  112000. 

8. 

43200  by  2340. 

16. 

932600  by  184900. 

17.  If  a  man  takes   180   steps  a  minute,  how 
many  steps  will  he  take  in  an  hour  ? 

18.  If  a  man  takes  2400  steps  a  mile,  how  many 
steps  will  he  take  in  walking  20  miles  ? 

19.  A  cat   has  18  toes.     How  many  toes  will 
6000  cats  have  ? 

20.  At  60  cents  a  yard,  what  will  be  the  cost  of 
digging  a  drain  350  yards  long  ? 


LESSON   44.  153 

If  one  or  both  factors  have  decimal  places : 

We  multiply  without  regard  to  the  decimal  point. 

Aftenvards  we  point  of  in  the  product  as  many 
decimal  places  as  there  are  decimal  places  in  the 
two  factors  together.     Thus  : 

Multiply  20.15  by  0.05. 

20.15 
0.05 


1.0075 


We  multiply  20.15  by  0.05  and  obtain  10075.  As  there  are  2 
decimal  places  in  the  multiplicand  and  2  in  the  multiplier,  we  point  off 
4  decimal  places  in  the  product  and  have  1.0075,  one  and  seventy-five 
ten-thousandths. 


SLATE 

EXERCISES. 

Multiply : 

1. 

0.541  by  444. 

13. 

22.74  by  0.525. 

2. 

0.853  by  232. 

14. 

3792  by  0.024. 

3. 

3764  by  0.47. 

15. 

0.715  by  141.5. 

4. 

32.12  by  1.73. 

16. 

466.4  by  45.06. 

5. 

7860  by  46.8. 

17. 

3.417  by  1000. 

6. 

0.623  by  373. 

18. 

0.955  by  10000. 

7. 

763.2  by  8.65. 

19. 

6781  by  1.007. 

8. 

68.42  by  75.5. 

20. 

527.1  by  0.103. 

9. 

8730  by  0.05. 

21. 

56.95  by  0.45. 

10. 

2.406  by  0.35. 

22. 

426.8  by  0.204. 

11. 

0.048  by  723. 

23. 

84.49  by  54.49. 

12. 

0.008  by  2.05. 

24. 

700.7  by  7.071. 

154  LESSON   45. 

SLATE   EXERCISES. 

1.  A  clock  that  strikes  the  hours,  and  1  for  the 
first  quarter,  2  for  the  second  and  3  for  the  third 
quarter,  of  each  hour,  strikes  300  times  a  day. 
How  many  times  will  it  strike  in  a  common  year  ? 

2.  A  clock  that  strikes  the  hours  only,  strikes 
156  times  in  a  day.  How  many  times  will  it  strike 
in  a  leap  year  ? 

3.  If  corn  is  $1.12  a  bag,  how  much  will  60 
bags  cost  ? 

4.  If  coal  is  $  5.75  a  ton,  how  much  will  17 
tons  cost  ? 

5.  If  pine  wood  is  $  3.50  a  cord,  how  much  will 
19  cords  cost  ? 

6.  A  farmer  has  37  acres  of  corn  worth  on  the 
average  $27  an  acre.  What  is  the  total  value  of 
his  corn  crop  ? 

7.  The  earth  moves  in  its  orbit  19  miles  a  sec- 
ond.    How  many  miles  does  it  move  in  1  minute  ? 

8.  If  a  bricklayer  earns  on  the  average  $  20.25 
a  week,  how  much  will  he  earn  in  28  weeks  ? 

9.  The  lunar  month  is  29.53  days.  How  many 
days  are  there  in  12  lunar  months  ? 

10.  Sound  travels  at  the  rate  of  1120  feet  a 
second.  Find  the  distance  of  a  thunder-cloud 
when  the  thunder  is  heard  13  seconds  after  the 
lightning  is  seen. 

11.  A  dealer  sold  27  bushels  of  potatoes  at  30 
cents  a  peck.     How  much  did  he  receive  ? 


LESSON   46.  155 

Divide  654  by  3. 

Here  6  -f-  3  =  2,  and  as  6  is  in  the  place  of  hundreds,  we  3)  654 
write  2  in  the  place  of  hundreds  under  the  6.  oTc 

Then  5  4-3  =  1,  with  remainder  2.  ^^^ 

We  write  the  1  in  the  place  of  tens,  under  the  5. 

The  remainder  2  is  2  tens  or  20  ones,  and  20  ones  put  with  the  4 
ones  make  24  ones. 

Then  24  -f-  3  =  8,  and  we  write  8  in  the  place  of  ones,  under  the  4. 

The  quotient,  therefore,  is  2  hundreds,  1  ten,  and 
8  ones  ;  that  is,  218. 

Divide  564  by  3. 

Here  5-^3  =  1,  with  remainder  2.  We  write  the  1  in  g'\  554 
the  place  of  hundreds,  under  the  6.  ^  ^^ 

The  remainder  2  is  2  hundreds,  or  20  tens,  and  20  tens  loo 

put  with  6  tens  make  26  tens. 

Then  26  -4-  3  =  8,  with  remainder  2. 

We  write  the  8  in  the  place  of  tens,  under  the  6. 

The  remainder  2  is  2  tens,  or  20  ones,  and  20  ones  put  with  4  ones 
make  24  ones. 

Then  24  h-  3  =  8,  and  we  write  8  in  the  place  of  ones,  under  the  4. 

The  quotient,  therefore,  is  1  hundred,  8  tens,  and 
8  ones  ;  that  is,  188. 

Divide  765  by  9. 

Since  7  will  not  contain  9,  we  take  for  the  first  par-  9)  765 
tial  dividend  76.  Then  76  -j-  9  =  8  with  remainder  4,  and  ^ — ^ 
as  6,  the  last  figure  of  this  dividend,  is  in  the  place  of  "^ 

tens,  we  write  the  quotient  8  in  the  place  of  the  tens  under 
the  6. 

The  remainder  4  is  4  tens  or  40  ones,  and  40  ones  put  with  the  5  ones 
make  45  ones. 

Then  45  -  9  =  5. 

Tlie  quotient,  therefore,  is  8  tens  and  5  ones ;  that 
is,  85. 


156 

LESSON  47. 

Divide  by  2  : 

468    456 

372 

332 

634 

972 

326    254 

214 

548 

418 

908 

Divide  by  3  : 

354    365 

624 

484 

408 

798 

444    235 

651 

790 

891 

976 

Divide  by  4 : 

924    824 

956 

564 

592 

918 

752    912 

734 

723 

712 

513 

Divide  by  5  : 

510    520 

640 

770 

590 

745 

665    735 

560 

880 

620 

825 

Divide  by  6  : 

666    636 

732 

726 

822 

924 

624    720 

744 

810 

846 

933 

Divide  by  7  : 

728    784 

812 

861 

910 

945 

742    797 

805 

875 

931 

952 

Divide  by  8  : 

808    832 

912 

336 

416 

256 

816    840 

920 

352 

424 

264 

Divide  by  9  : 

927    945 

405 

378 

288 

135 

936    918 

396 

387 

297 

225 

LESSON   48. 


157 


SHORT  I>IVISIOX. 

When  the  divisor  is  so  small  that  the  work  can  be 
performed  mentally,  the  process  is  called  short  division. 


Divide  63169  by  7. 

7)63169 

9024  with  rem.  1. 


Wording  :  7  in  63,  9  ;   in  1,  0  ;  in  10 
2  ;  in  29,  4  ;  witli  rem.  1. 

ExpLAXATioN :  Since  7  is  not  con- 
tained in  6,  we  take  two  figures  63  for 
the  first  partial  dividend,  and  write  the 
quotient  9  under  the  right-hand  figure  3  of  this  partial  dividend.  7  is 
not  contained  in  1 ,  so  0  is  written  as  the  second  figure  of  the  quotient, 
and  this  1,  which  is  equal  to  10  units  of  the  next  lower  order  of  units, 
is  joined  to  the  6,  and  makes  16  for  the  next  partial  dividend.  Then 
16  is  divided  by  7  ;  the  quotient  is  2  and  the  remainder  2  ;  the  remain- 
der 2  is  equal  to  20  of  the  next  lower  order  of  units,  and  with  the  9 
makes  29.  Then  29  is  divided  by  7  ;  the  quotient  is  4  and  the  remain- 
der 1.     Therefore  the  quotient  is  9024,  and  the  remainder  is  1. 

To  prove  division,  we  find  the  product  of  tlie  divisor 

and  quotient,  and  to  this  product  add  the  remainder. 

The  result  should  be  equal  to  the  dividend. 


Proof. 


9024 

7 

63168 
1 

63169 


The  product  of  the  divisor  and  quotient  is 
G3168. 

To  this  product  add  the  remainder  1,  and 
the  result  is  63169,  the  same  as  the  dividend. 


Divide  $54322  by  19. 

$9)854322 

6035  with  $7  rem. 

In  this  example  we  are  required 
to  find  the  number  of  times  we  can 
take  away  $9  from  .$  54322.  The 
answer  is  6035  times,  with  $7 
over.  The  complete  quotient  may 
be  written  6035f 


Divide  $54322  by  9. 

9)  $54322 

$6035  with  $7  rem. 

In  this  example  we  are  required 
to  divide  $54322  into  nine  eqnal 
parts,  and  to  find  the  number  of 
dollars  in  each  part.  The  answer 
is  6035  dollars,  with  $  7  over.  The 
answer  may  be  written  .^i  6035|. 


158  LESSON   49. 


The  last  two  examples  illustrate  the  dif 

ferent  mean- 

ings  of  division. 

If  the  divisor  and  dividend  refer  to  the 

same  kind  of  units,  the 

quotient  denotes  the  number  of 

times  the  divisor 

must  be  taken  tc 

>  equal  1 

:he  dividend. 

If  the  divisor  is 

an  abstract  number  as  2,  i 

B,  4,  etc.,  the 

quotient  denotes 

a  number  of  units 

of  the  same  kind  as 

the  units  of  the  dividend. 

Divide  : 

1.   434  by  2. 

23. 

5794  by  2. 

45. 

95874  by  2. 

2.   876  by  3. 

24. 

5874  by  3. 

46. 

45873  by  3. 

3.   596  by  4. 

25. 

5696  by  4. 

47. 

46372  by  4. 

4.   432  by  4. 

26. 

8975  by  5. 

48. 

78295  by  5. 

5.    180  by  5. 

27. 

3354  by  6. 

49. 

66372  by  6. 

6.    715  by  5. 

28. 

1176  by  7. 

50. 

92582  by  7. 

7.    875  by  5. 

29. 

8568  by  8. 

51. 

87824  by  8. 

8.   618  by  6. 

30. 

2943  by  9. 

52. 

98172  by  9. 

9.   324  by  6. 

31. 

3711  by  2. 

53. 

78956  by  7. 

10.    819  by  7. 

32. 

3226  by  3. 

54. 

65978  by  8. 

11.    847  by  7. 

33. 

8467  by  4. 

55. 

76598  by  6. 

12.    920  by  8. 

34. 

9573  by  5. 

56. 

83621  by  3. 

13.   904  by  8. 

35. 

6983  by  6. 

57. 

86123  by  6. 

14.    945  by  9. 

36. 

8659  by  7. 

58. 

38612  by  9. 

15.    621  by  9. 

37. 

4329  by  8. 

59. 

12386  by  7. 

16.   513  by  2. 

38. 

8256  by  9. 

60. 

50080  by  8. 

17.   707  by  3. 

39. 

5879  by  3. 

61. 

65387  by  7. 

18.   845  by  4. 

40. 

7361  by  9. 

62. 

75429  by  5. 

19.    901  by  5. 

41. 

6539  by  8. 

63. 

31285  by  6. 

20.    862  by  6. 

42. 

5396  by  7. 

64. 

29514  by  9. 

21.    872  by  7. 

43. 

9751  by  3. 

65. 

65387  by  8. 

22.    907  by  9. 

44. 

6857  by  7. 

66. 

57148  by  3. 

LESSON   50. 


159 


LONG  DIVISION. 

The  process  of  Long  Division  is  the  same  as  that  of 
Short  Division,  except  that  the  work  is  written  in  full, 
and  the  quotient  is  written  over  the  dividend. 

Divide  31864  by  87. 

The  beginner  will  find  it  convenient  to  form  a  table  of  products  of 

the  divisor  by  the  numbers  1,  2,  3,  ...,  as  follows: 


1    1  X  87  =  87 

4  X  87  =  348 

7  X  87  =  009 

2  X  87  =  174 

6  X  87  =3  435 

8  X  87  =  696 

3  X  87  =  261 

6  X  87  =  522 

9  X  87  =  783 

As  87  is  more  than  31,  it  is  necessary  to  take  three  figures  of  the 
dividend  for  the  first  partial  dividend.    Of  the  products  in  the  table 


OPERATION. 

366 
87)31864 
261 
576 
522 
544 
522 
22  rem. 


that  do  not  exceed  318,  the  greatest  is  261  ; 
that  is,  3  X  87.     Hence  the  first  quotient  figure 
is  3,   and  is  written  over  the  8,  the  right, 
hand  figure  of  the  first  partial  dividend  ;  then 
261  is  subtracted  from  318.     To  the  remain- 
der 57,  the  next  figure  6  of  the  dividend  is 
annexed.     Of  the  products  that  do  not  exceed 
576,  the  greatest  is  522  ;  that  is,  6x87.    Hence 
6  is  the  next  figure  of  the  quotient,  and  the  next 
remainder  is  54,  to  which  the  4  of  the  dividend 
is  annexed.    Of  the  products  that  do  not  ex- 
ceed 544,  the  gTcatest  is  522  ;  that  is,  6  x  87.     Hence  the  next  figure 
of  the  quotient  is  6,  and  the  remainder  22.     Therefore  the  quotient  is 
366,  and  the  remainder  22. 

After  a  little  practice  the  operation  of  division  can 
be  performed  without  the  aid  of  a  table  of  products. 

If  at  any  step  the  product  is  greater  than  the  partial 
dividend,  the  number  denoted  by  the  quotient-figure 
is  too  large  and  must  be  diminished ;  if  the  remainder  is 
greater  than  the  divisor,  the  number  denoted  by  the 
quotient-figure  is  too  small  and  must  be  increased. 


160  LESSON   51. 

Divide  1006078  by  247. 

The  first  partial  dividend  is  1006.     We  find  that  5  x  247  is  1235, 

OPERATION.  which  is  greater  than  1006,  and  therefore  5 

Af\no  is  too  large.    We  try  4,  and  find  that  4  x  247 

^^LIA  is  988.     We  write  the  4  over  the  6,   the 

z47}10Ud07o  right-hand  figure  of  the  partial  dividend, 

988  and  subtract  the  988  from  1006.    To  the 

1807  remainder  18  we  annex  0,  the  next  figure 

1729  of  the  dividend,  and  have  180.      Since  247 

<7QQ  is  not  contained  in  180,  we  write  0  for  the 

rjA-t  next  figure  of  the  quotient,  and  annex  to 

— — -  180  the  next  figure  of  the  dividend,  7.    The 

4<  rem.  j^g^t  figure  of  the  quotient  is  not  9,  for 
9x247=2223,  and  is  not  8,  for  8x247  =  1976,  and  each  of  these  prod- 
ucts is  greater  than  1807.  We  try  7,  and  find  the  product  to  be  1729, 
which  is  less  than  1807.  The  remainder  obtained  by  subtracting  1729 
from  1807  is  78,  to  which  we  annex  the  8  of  the  dividend,  and  have 
788.  The  next  figure  of  the  quotient  is  3,  and  the  product  of  3  x  247 
is  741.  Subtracting  741  from  788  we  get  47  for  the  remainder  of  the 
division.     Hence  the  quotient  is  4073,  and  the  remainder  47. 

Divide  : 

1.  5938  by  36.  13.  8757  by  67.  25.  8332  by  71. 

2.  5743  by  37.  14.  9212  by  91.  26.  9888  by  93. 

3.  9853  by  49.  15.  2786  by  22.  27.  7112  by  43. 

4.  7369  by  52.  IG.  3764  by  29.  28.  2931  by  19. 

5.  9423  by  63.  17.  6753  by  57.  29.  9213  by  29. 

6.  6578  by  74.  18.  9362  by  89.  30.  8778  by  55. 

7.  6457  by  59.  19.  8579  by  73.  31.  61238  by  101. 

8.  3579  by  21.  20.  8957  by  79.  32.  86123  by  201. 

9.  7436  by  34.  21.  7319  by  53.  33.  38612  by  302. 

10.  4589  by  42.   22.  8609  by  61.   34.  23816  by  205. 

11.  5936  by  47.   23.  6891  by  31.   35.  12386  by  502. 

12.  8372  by  65.   24.  3954  by  23.   36.  83216  by  603. 


LESSON  52. 

1. 

98245  by  704. 

28. 

200836  by  897. 

2. 

59824  by  215. 

29. 

650734  by  635. 

3. 

45982  by  316. 

30. 

573206  by  753. 

4. 

82459  by  638. 

31. 

732065  by  537. 

5. 

93827  by  859. 

32. 

723540  by  871. 

6. 

96548  by  789. 

33. 

680023  by  997. 

7. 

84596  by  627. 

34. 

650734  by  736. 

8. 

23469  by  295. 

35. 

572036  by  853. 

9. 

24963  by  468. 

36. 

704532  by  973. 

10. 

59376  by  261. 

37. 

432960  by  187. 

11. 

56379  by  237. 

38. 

349062  by  259. 

12. 

79476  by  732. 

39. 

802365  by  795. 

13. 

67532  by  557. 

40. 

690409  by  389. 

14. 

70456  by  678. 

41. 

109370  by  167. 

15. 

80026  by  709. 

42. 

963047  by  398. 

16. 

72345  by  567. 

43. 

750431  by  578. 

17. 

90365  by  463. 

44. 

895047  by  757. 

18. 

78659  by  741. 

45. 

938704  by  198. 

19. 

94158  by  429. 

46. 

618543  by  4021. 

20. 

48519  by  229. 

47. 

816354  by  2008. 

21. 

67857  by  479. 

48. 

543168  by  4307. 

22. 

99321  by  912. 

49. 

604307  by  4803. 

23. 

79132  by  811. 

50. 

729718  by  5184. 

24. 

83742  by  566. 

51. 

542385  by  4978. 

25. 

650734  by  537. 

52. 

604730  by  4758. 

26. 

732065  by  631. 

53. 

817279  by  9814. 

27. 

704523  by  873. 

54. 

729718  by  4918. 

161 


162  LESSON   53. 

ORAL.  EXERCISES. 

1.  If  3  cords  of  wood  cost  $  9,  what  will  4  cords  cost? 

Note.  Require  the  pupil  to  analyze  this  and  similar  problems  by 
the  unitary  method.  Thus,  if  3  cords  cost  $9,  1  cord  will  cost  |  of 
$  9,  or  $  3  ;  and  4  cords  will  cost  4  x  1 3,  or  $  12. 

2.  If  4  men  can  mow  a  field  in  6  days,  how  many 
days  will  it  take  3  men  to  mow  the  field  ? 

Analysis.  If  it  takes  4  men  6  days  to  mow  a  field,  it  will  take  1  man 
4x6  days,  or  24  days  ;  if  it  takes  1  man  24  days  to  mow  a  field,  it 
will  take  3  men  i  of  24  days,  or  8  days. 

3.  Find  the  cost  of  7  barrels  of  flour,  if  8  barrels  cost 
$40. 

4.  Find  the  cost  of  12  oranges,  if  5  oranges  cost  15 
cents. 

5.  What  will  12  lambs  cost,  if  3  lambs  cost  |12? 

6.  If  12  men  can  dig  a  certain  ditch  in  6  days,  how 
many  men  will  be  required  to  dig  the  ditch  in  8  days  ? 

7.  If  8  pounds  of  sugar  cost  40  cents,  how  many 
cents  will  11  pounds  cost? 

8.  If  3  tons  of  coal  cost  $  21,  how  much  will  8  tons 
cost? 

9.  If  4  men  can  build  a  wall  in  5  days,  how  many 
men  will  be  required  to  build  it  in  4  days  ? 

10.  If  3  yards  of  cloth  are  worth  $6,  how  much  are 
7  yards  worth  ? 

11.  If  2  lamps  cost  $  8,  what  will  5  lamps  cost  ? 

12.  If  9  yards  of  muslin  cost  63  cents,  what  will  8 
yards  cost  ? 

13.  If  8  men  can  do  a  piece  of  work  in  9  days,  how 
many  days  will  it  take  6  men  to  do  it  ? 

14.  How  many  pounds  of  butter  at  20  cents  a  pound 
must  be  given  for  2  pounds  of  tea  at  60  cents  a  pound? 


Part  IV. 

LESSON   1. 

DIVISION  OF  DECIMALS. 

In  Division,  if  the  dividend  and  divisor  are  both  mul- 
tiplied or  both  divided  by  the  same  number,  the  quotient 
is  not  changed.  Thus,  18-!- 6  =  3,  and  (when  both  divi- 
dend and  divisor  are  multiplied  by  2)  36-^12  =  3. 
Again  (when  both  dividend  and  divisor  are  divided 
by  2),  9-3  =  3. 

If  the  divisor  is  a  whole  number,  and  the  dividend  has 
decimals  :  We  divide  as  in  ivhole  numbers^  hut  2vrite  the 
decimal  point  in  the  quotient  as  soo7i  as  the  decimal  point 
in  the  dividend  is  reached. 

Divide  1.29  by  3. 

3)1.29  Since  3  is  not  contained  in  1,  we  write  0  under  the  1  ; 

A  Ao      then  the  decimal  point,  and  afterwards  we  continue,  3  in 
12,  4  ;  3  in  9,  3.     The  quotient  is  43  hwidredths. 

Divide : 

1.  3.27  by  3.  8.  89.6  by  32.  15.  416.64  by  112. 

2.  4.64  by  4.  9.  17.92  by  16.  16.  4089.8  by  121. 

3.  5.75  by  5.  10.  313.6  by  14.  17.  17.161  by  131. 

4.  16.24  by  7.  11.  375.7  by  17.  18.  380.48  by  232. 

5.  18.66  by  6.  12.  709.5  by  15.  19.  140.36  by  116. 

6.  18.48  by  8.  13.  42.12  by  18.  20.  140.30  by  115. 

7.  28.17  by  9.  14.  8.489  by  13.  21.  2702.7  by  117. 

163 


164  LESSON   2. 

If  the  divisor  has  decimals,  and  the  dividend  is  a  whole 
number  :  We  annex  as  many  zeros  to  the  dividend  as  there 
are  decimal  places  in  the  divisor,  and  remove  the  decimal 
point  from  the  divisor. 

Divide  129  by  0.2. 

2)1290  Here  we  add  0  to  the  129,  making  1290,  and  divide  by 

nAr      2  ;  in  other  words,  we  multiply  both  dividend  and  divisor 
by  10. 

Divide : 

1.  129  by  0.3.  8.  132  by  0.33.  15.  121  by  0.11. 

2.  122  by  0.4.  9.  625  by  2.5.  16.  132  by  0.12. 

3.  136  by  0.5.  10.  603  by  1.5.  17.  169  by  0.13. 

4.  174  by  0.6.  11.  165  by  3.3.  18.  196  by  1.4. 

5.  161  by  0.7.  12.  282  by  4.7.  19.  256  by  0.16. 

6.  128  by  0.8.  13.  318  by  5.3.  20.  324  by  1.8. 

7.  117  by  0.9.  14.  648  by  7.2.  21.  585  by  Q.b, 

li  both  the  divisor  and  dividend  have  decimals  :  We 
remove  the  decimal  point  from  the  divisor,  and  move  the 
decimal  point  in  the  dividend  to  the  right  as  many  places 
as  there  are  decimals  in  the  divisor. 

Divide  1.29  by  0.3. 

3)12.9  Here  we  carry  the  decimal  point  in  the  dividend  one 

7~o      place  to  the  right,  and  remove  it  from  the  divisor.    In  other 
words,  we  multiply  both  dividend  and  divisor  by  10. 

Divide  : 

22.  12.9  by  0.3.  28.  3.24  by  0.9.  34.  0.96  by  0.2. 

23.  12.4  by  0.4.  29.  13.2  by  0.3.  35.  0.33  by  0.3. 

24.  13.5  by  0.5.  30.  2.01  by  0.5.  36.  1.98  by  0.9. 

25.  1.86  by  0.6.  31.  1.28  by  0.4.  37.  17.6  by  0.8. 

26.  1.61  by  0.7.  32.  17.4  by  0.6.  38.  15.5  by  0.05. 

27.  12.8  by  0.8.  33.  1.82  by  0.7.  39.  12.6  by  0.09. 


LESSON   3.  165 

Divide  28.3696  by  1.49. 

OPERATION. 

19.04 
149)2836.96 
149 
1346 
1341 


596 
596 


Here  the  decimal  point  is  removed  from  the  divisor,  and  is  moved 
two  places  to  the  right  in  the  dividend  ;  in  other  words,  both  dividend 
and  divisor  are  multiplied  by  100. 


Find  the  quotients  of 

1. 

80.24^8. 

17. 

300 -^  0.015. 

2. 

12.5664-1-4. 

18. 

32-0.064. 

3. 

1301.4-241. 

19. 

2.88 -^  0.0024. 

4. 

2647.08^324. 

20. 

6.2-0.0025. 

5. 

9.215^0.08. 

21. 

65.1021-3.207. 

6. 

664.56-0.18. 

22. 

7704.256-928. 

7. 

132.6-425. 

23. 

506.016^753. 

8. 

7.48^0.085. 

24. 

1.9248-^-0.008. 

9. 

0.748^44. 

25. 

62825^1.75. 

10. 

2878.2-369. 

26. 

700727 -J- 0.029. 

11. 

2.3328-0.36. 

27. 

276.766-- 37.1. 

12. 

52.5-0.025. 

28. 

0.1024-2.56. 

13. 

1521-11.7. 

29. 

1024--25.6. 

14. 

7236-^1.44. 

30. 

1292 --3.23. 

15. 

67288^64.7. 

31. 

906.5^0.185. 

16. 

73807-^0.023. 

32. 

0.4496 -^  11.24. 

166  LESSON   4. 

SLATE  EXERCISES. 

1.  A   box  contains   1416  eggs.     How  many  dozen 
eggs  are  there  in  the  box? 

2.  If  13  yards  of  velvet  cost  197.50,  what  is  the 
price  of  one  yard  ? 

3.  If  '138,057  are  divided  into  19  equal  parts,  how 
many  dollars  will  there  be  in  each  part? 

4.  How  many  times  is  the  sum  of  $17  contained  in 
12890? 

5.  There  are  320  rods  in  a  mile.     How  many  miles 
are  there  in  9280  rods  ? 

6.  At  $16.50  a  ton,  how  many  tons  of  hay  can  be 
bought  for  1 280.50? 

7.  At  $5.75  a  ton,  how  many  tons  of  coal  can  be 
bought  for  $103.50? 

8.  At  24  cents  a  dozen,  how  many  dozen  eggs  can 
be  bought  for  1 61.44? 

9.  I  bought  96  shares  of  railroad  stock  for  $12,000. 
How  much  did  the  stock  cost  a  share  ? 

10.  If  a  field  produces  4905  bushels  of  corn,  produc- 
ing on  the  average  45  bushels  to  the  acre,  how  many 
acres  does  the  field  contain  ? 

11.  At  $  10.50  a  ton,  how  many  tons  of  plaster  can  be 
bought  for  $65,625? 

12.  A  man  bought  a  barrel  of  sugar,  weighing  232 
pounds,  for  $12.76.  How  many  cents  a  pound  did 
he  pay  for  the  sugar  ? 

13.  When  the  price  of  Messina  oranges  is  $2.75  a 
box,  how  many  boxes  can  be  bought  for  $77  ? 

14.  In  how  many  hours  will  a  cistern  holding  4200 
gallons  be  filled  by  a  pipe  that  discharges  into  it  175 
gallons  an  hour  ? 


LESSON   5.  167 

Tf  the  divisor  is  not  contained  in  the  dividend  with- 
out a  remainder,  zeros  may  be  annexed  to  the  dividend, 
and  the  division  continued. 

Divide  0.39842  by  3.7164  to  four  decimal  places. 

OPERATION. 

0.1072 


37164)  3984.2 
3716  4 


267800 
260148 


76520 

74328 

2192 

If  the  divisor  is  a  whole  number,  and  ends  in  zeros. 

We  cut  off  the  zeros  fro7n  the  divisor^  and  move  the  decimal 
pomt  in  the  dividend  as  many  places  to  the  left  (^prefixing 
zeros  if  necessary)^  as  there  are  zeros  cut  off. 

Divide  42.08  by  8000. 

Ol'EKATION. 

8)  0.04208 
0.00526 

Here  the  three  zeros  are  cut  off  from  the  divisor,  and  the  decimal 
point  in  the  dividend  is  moved  three  places  to  the  left.  In  other 
words,  both  divisor  and  dividend  are  divided  by  1000. 

SLATE  EXERCISES. 
Divide  to  four  decimal  places  : 

1.  5.8  by  4.79.  6.  8.6  by  3000. 

2.  7.34  by  2.3.  .    7.  95  by  7000. 

3.  16.28  by  0.67.  8.  89  by  6700. 

4.  54.87  by  0.39.  9.  0.32  by  410. 

5.  2.86  by  349.  10.  0.51  by  3700. 


168  LESSON   6. 

SLATE  EXERCISES. 

1.  The  production  of  pig-iron  in  the  United  States  for 
the  census  year  of  1890  was  9,579,779  tons,  and  3,781,- 
021  tons  for  the  census  year  of  1880.    Find  the  increase. 

2.  In  1880  Alabama  produced  62,336  tons  of  pig-iron, 
and  890,432  tons  in  1890.  How  many  times  the  pro- 
duction of  1880  is  the  production  of  1890  ? 

3.  The  production  of  steel  rails  in  the  United  States 
in  1880  was  741,475  tons,  and  2,036,654  tons  in  1890. 
Find  the  increase. 

4.  The  value  of  wool  manufactures  in  the  United 
States  for  the  census  year  of  1890  was  1337,768,524;  of 
cotton  manufactures  $267,981,724  ;  of  silk  manufactures 
187,298,454.  Find  the  total  value  of  the  products  of 
these  three  industries. 

5.  Find  the  difference  in  value  between  the  wool 
and  the  cotton  manufactures  of  the  United  States  in 
1890. 

6.  The  total  area  devoted  to  the  cultivation  of 
cereals  in  the  New  England  States  in  1889  was  580,297 
acres,  and  in  1879  the  total  area  was  746,128  acres. 
Find  the  decrease. 

7.  In  1889  New  Hampshire  raised  988,806  bushels 
of  Indian  corn  from  23,746  acres.  Find  to  two  places  of 
decimals  the  average  number  of  bushels  per  acre. 

8.  In  1889  Iowa  raised  313,130,782  bushels  of  Indian 
com  from  7,585,522  acres.  Find  to  the  nearest  bushel 
the  average  number  of  bushels  per  acre. 

9.  In  1889  the  United  States  raised  468,321,424 
bushels  of  wheat  from  33,575,898  acres.  Find  to  the 
nearest  bushel  the  average  number  of  bushels  per  acre. 


LESSON   7.  169 

COMPOUND    QUANTITIES. 

A  quantity  expressed  in  a  single  unit  is  called  a  sim- 
ple quantity  ;  but  a  quantity  expressed  in  different  units 
is  called  a  compound  quantity. 

Thus,  20 1  pounds  is  a  simple  quantity,  but  20  pounds  4  ounces  is  a 
compound  quantity. 

A  unit  of  greater  value  or  measure  than  another  is 
said  to  be  of  a  higher  denomination  than  the  other. 

Thus,  the  dollar  is  of  a  higher  denomination  than  the  cent,  the  pound 
than  the  ounce,  the  yard  than  the  inch,  the  hour  than  the  minute. 

The  process  of  changing  the  denomination  in  which  a 
quantity  is  expressed,  without  changing  the  value  of  the 
quantity  is  called  reduction. 

If  the  change  is  from  a  higher  denomination  to  a 
lower,  it  is  called  reduction  descending ;  if  from  a  lower 
to  a  higher,  it  is  called  reduction  ascending. 

Thus,  1  yard  =  36  inches  is  an  example  of  reduction  descending ; 
and  24  inches  =  2  feet  is  an  example  of  reduction  ascending. 

OQUID  MEASURE. 

Liquid  Measure  is  used  in  measuring  liquids,  as  water, 
milk,  etc. 

Table. 
4  gills  (gi.)  =  1  pint  (pt.). 
2  pints  =  1  quart  (qt.). 

4  quarts       =  1  gallon  (gal.).  . 
Hence,  1  gal.  =  4  qts.=  8  pts.  =  32  gi. 


31^  gals.       =  1  barrel  (bbl.). 

63  gals.  =  1  hogshead. 
Note.  Casks  holding  from  28  gals,  to  43  gals,  are  called  barrels, 
and  casks  holding  from  54  gals,  to  63  gals,  are  called  hogsheads.  If 
we  say,  however,  that  a  cistern  holds  100  barrels,  we  mean  barrels  of 
31 1  gals,  each ;  or  if  we  say  that  a  cistern  holds  100  hogsheads,  we 
mean  hogsheads  of  63  gals.  each. 


170  LESSON   8. 

Reduce  10  gallons  3  quarts  1  pint  to  i)ints. 

gals.    qts.     pts. 

10     3     1 

4  10  gals.  =  10  X  4  qts.  =  40  qts. ,  and  40  qts.  with  the 

— —  3  qts.  added  are  43  qts. 

^^  43  qts.  =  43  X  2  pts.  =  86  pts.,  and  86  pts.  with  the 
^  1  pt.  added  are  87  pts. 

8T  87  pts.  Ans. 

Hence  in  reduction  descending  :  We  7nultiply  the  given 
number  of  highest  units  hy  the  number  of  the  next  lower 
units  required  to  7nake  one  of  this  higher ;  and  add  to 
the  product  the  given  number  of  this  lotver  unit. 

We  proceed  in  this  wag  with  each  successive  result^  until 
the  required  unit  is  reached. 

Reduce : 

1.  5  qts.  3  pts.  to  pints.  5.  8  gals.  1  pt.  to  pints. 

2.  3  qts.  1  pt.  to  pints.  6.  11  gals.  1  qt.  to  pints. 

3.  7  gals.  1  pt.  to  pints.  7.  2  bbls.  to  quarts. 

4.  1  gal.  1  pt.  to  gills.  8.  3  hhds.  to  pints. 

Reduce  129  pints  to  higher  units. 

2  129  pts.  129  pts.  =  1-1^  qts.  =  64  qts.  and  1  pt.  over. 

4     64  qts.  ...  1  pt.         64  qts. =-\*  gals.  =  16  gals,  and  no  qts.  over. 
16  gals.  .  .  0  qts.  16  gals.  0  qts.  1  pt.   Ans. 

Hence  in  reduction  ascending  :  We  divide  by  the  given 
number  of  units  required  to  make  one  of  the  7iext  higher. 

We  divide  this  quotient^  and  each  successive  quotient  in 
like  manner^  until  the  required  unit  is  reached. 

The  last  quotient  and  the  several  reiyiainders  arranged 
in  order  is  the  answer  sought. 

Reduce  to  higher  units  : 
9.    229  pints.  11.    365  pints.  13.    1052  pints. 

10.   51  pints.  12.   442  pints.  14.   1727  gills. 


gals. 

qts. 

l)t8. 

4 

3 

1 

11 

1 

0 

3 

1 

25 

2 

1 

LESSON   9.  171 

Add  4  gals.  3  qts.  1  pt. ;  11  gals.  1  qt. ;  3  qts.  1  pt. ; 
and  25  gals.  2  qts.  1  pt. 

Write  the  quantities  so  that  units  of  the  same  name 
shall  be  in  the  same  column. 

The  sum  of  the  pints  is  S.  Divide  the  3  pts.  by  2 
(2  pts.  =  1  qt.).  The  result  is  1  qt.  and  1  pt.  Write 
the  1  pt.  under  the  column  of  pints. 

The  sum  of  the  quarts,  including  1  qt.  from  the  3  pts. , 
■^2  2  1  is  10.  Divide  the  10  qts.  by  4  (4  qts.  =  1  gal.).  The 
result  is  2  gals,  and  2  qts.  Write  the  2  qts.  under  the  column  of  quarts, 
and  add  the  2  gals,  to  the  gallons  in  the  coluuni  of  gallons. 

42  gals.  2  qts.  1  pt.  Ans. 

From  4  gals.  2  qts.  1  pt.  take  2  gals.  3  qts.  1  pt. 

gals.  qts.  pts.  Since  1  pt.  —  1  pt.  is  0  pt. ,  write  0  under  the  column 

4      2  1  of  pints. 

2  3  1  Since  3  qts.  are  more  than  2  qts.,  take  1  gal.  from 
~  ~  ~  the  4  gals.,  reduce  it  to  quarts,  and  add  them  to  the 
1      ^  ^  2  qts.,  making  6  qts.     Then,  6  qts.  -  3  qts.  =  3  qts. 

Write  3  under  the  column  of  quarts.    Then  3  gals.  —  2  gals.  =  1  gal. 

1  gal.  3  qts.  Ans. 
Add: 

1.  2.  3. 

gals.   qts.   pts.  gals.     qts.     pts.  gals.     qts.     pts. 

3  11  21     3     n  43     1     1 

7  3     1  18     2    1}  27     3     1 

8  3     1  7     2     1  31     3     11 


Find  the  difference 

)  between: 

4. 

5. 

6. 

gals. 

qts. 

pts. 

gals. 

qts. 

pts. 

gals. 

qts. 

pts. 

21 

2 

1 

18 

2 

0 

27 

2 

1^ 

7 

3 

1 

7 

2 

1 

17 

3 

r 

7.  From  a  barrel  that  held  just  40  gals,  and  2  qts.  of 
vinegar  there  were  drawn  19  gals,  and  1  pt.  How  much 
vinegar  was  left  in  the  barrel  ? 


172  LESSON    10. 

Multiply  27  gals.  3  qts.  1  pt.  by  5. 

gals.    qts.    ptB.  5  X  1  pt.  =  5  pts.  =  2  qts.  1  pt.     Write  the  1  pt. 

27      3      1       under  the  pints,  and  reserve  the  2  qts.  to  be  added  to 

5       the  product  of  5  x  3  qts. 

-joq      ^       7  5x3  qts.  =  15  qts.,  and  15  qts.  +  2  qts.  =  17  qts. 

=  4  gals,  1  qt. 

Write  the  1  qt.  under  the  quarts  and  add  the  4  gals,  to  5  x  27  gals. 

139  gals.  1  qt.  1  pt.  Ans. 
Divide  113  gals.  2  qts.  by  4. 

gals.      qts.    pts.  The  quotient  from  dividing  113  gals,  by  4  is 

4)113       2      0         28  gals.,  and  the  remainder  is  1  gal. 

28       1      1  Keduce  the  1  gal.  to  quarts,  and  add  them  to 

the  2  qts.     The  sum  is  6  qts. 
The  quotient  from  dividing  6  qts.  by  4  is  1  qt.,  and  the  remainder 
is  2  qts. 

Reduce  the  2  qts.  to  pints,  and  we  have  4  pts.  Then  4  pts.  -f-  4 
=  1  pt. 

28  gals.  1  qt.  1  pt.  An%. 

Divide  12  gals.  1  qt.  by  3  qts.  1  pt. 

12  gals.  1  qt.  =  49  qts.  =  98  pts. 
3  qts.    1  pt.  =7  pts. 

and  98  H-  7  =  14.  Ans. 

Multiply  : 

1.  7  gals.  3  qts.  1  pt.  by  9. 

2.  31  gals.  2  qts.  by  7. 

3.  3  qts.  1  pt.  3  gi.  by  8. 
Divide  : 

4.  126  gals.  3  qts.  1  pt.  by  6. 

5.  110  gals.  1  qt.  by  7. 

6.  131  gals,  by  8. 

Note.  Methods  precisely  similar  to  the  preceding  are  employed  for 
the  reduction,  addition,  subtraction,  multiplication,  and  division  of  all 
compound  quantities. 


LESSON   11.  173 

DRY    MEASURE. 

Dry  Measure  is  used  in  measuring  dry  articles,  as 
grain,  seeds,  fruit,  vegetables. 

Table. 

2  pints  (pt.)  =  1  quart  (qt.). 

8  quarts         =  1  peck  (pk.). 

4  pecks  =  1  bushel  (bu.). 

Hence  1  bu.  =  4  pks.  =  32  qts. 

NoTK  1.  The  gallon  of  liquid  measure  contains  231  cubic  inches. 
Therefore  the  quart  of  liquid  measure  contains  57 1  cu.  in.  The  bushel 
of  dry  measure  contains  2150.42  cubic  inches.  Therefore,  the  quart  of 
dry  measure  contains  67  i  cu.  in. 

Note  2.  In  measuring  grain,  seeds,  and  small  fruits,  the  measure 
must  be  even  full.  In  measuring  apples,  potatoes,  and  other  large 
articles,  the  measure  must  be  heaping  full. 

1.  Reduce  5  bu.  3  pks.  4  qts.  to  quarts. 

2.  Reduce  4056  pts.  to  higher  denominations. 

3.  Multiply  7  bu.  2  pks.  7  qts.  by  9. 

4.  Divide  25  bu.  3  pks.  2  qts.  by  7. 

5.  How  many  4-quart  measures  will  2  bu.  2  pks.  4  qts. 

mi? 

6.  Divide  20  bu.  2  pks.  by  8. 
Add: 


7. 

8. 

9. 

bu.    pks.   qts. 

5     13 
3     3     3 

7     2     7 

bu.    pks. 

8  3 

9  3 
9     3 

qts. 
1 

7 
6 

bu.      pks. 

121     1 
156     3 
132     3 

qts. 

7 
6 
5 

Subtract : 

10. 

11. 

12. 

bu.    pks.   qts. 

5     2     2 
3     17 

bu.    pks. 

8     1 
4     3 

qts. 

2 
3 

bu.      pks. 

150     2 
136     3 

qts. 

5 

7 

174  LESSON   12. 

AVOIRDUPOIS    WEIGHT. 

Avoirdupois  Weight  is  used  in  weighing  all  articles 
except  gold,  silver,  and  precious  stones. 

Tablk. 

16  ounces  (oz.)  =  1  pound  (lb.). 

2000  pounds  =  1  ton  (t.) . 

The  long  ton  is  used  in  the  United  States  Custom  Houses  and  in 
wholesale  transactions  in  iron  and  coal. 

112  pounds  Avoirdupois  =  1  long  hundredweight  (cwt). 
2240  pounds  Avoirdupois  —  1  long  ton. 


1  pound  Avoirdupois    =  7000  gi-ains. 
Note.    Many  articles  are  sold  by  weight,  as  follows  : 


1  bu.  of  wheat  or  beans  =  60  lbs, 

1  bu.  of  corn  or  rye  =  56  lbs. 

1  bu.  of  corn  or  rye  1  ^  5Q  ^^^ 

meal  or  cr'ked  corn  / 

1  bu.  of  oats  =  82  lbs. 

1  bu.  of  barley  =  48  lbs. 

1  bu.  of  timothy  seed  =  45  lbs. 


1  bu.  of  potatoes  =    60  lbs. 

1  barrel  of  flour  =  196  lbs. 
1  barrel  of  beef  or  pork  =  200  lbs. 

1  cask  of  lime  =  240  lbs. 

1  quintal  of  fish  =  100  lbs. 

1  stone  of  iron  or  lead  =    14  lbs. 

1  pig  of  iron  or  lead  =  300  lbs. 


1.  Reduce  3  long  tons  12  cwt.  110  lbs.  to  pounds. 

2.  Reduce  87,956  lbs.  of  coal  to  long  tons. 

3.  Multiply  3  t.  1200  lbs.  of  hay  by  5. 

4.  Divide  8  t.  1500  lbs.  of  hay  by  7. 

5.  Add  1  t.  1326  lbs.,  1 1.  1560  lbs.,  1  t.  1728  lbs. 

6.  From  2  t.  1015  lbs.  take  1  t.  515  lbs. 

7.  From  a  firkin  of  butter  containing  42  lbs.  there 
were  sold  13  lbs.  10  oz.     How  much  was  left  ? 

8.  At  23  cents  a  pound,  what  will  3.5  lbs.  of  steak 
cost? 

9.  At  115  a  ton,  what  will  3.75  tons  of  hay  cost? 


LESSON  13.  175 

TROY    WEIGHT. 

Troy  Weight  is  used  in  weighing  gold,  silver,  and 
precious  stones. 

Tablk. 

24  grains  (grs.)      =  1  pennyweight  (dwt.). 
20  pennyweights    =  1  ounce  (oz.) . 
12  ounces*  =  1  pound  (lb.). 

The  pound  Troy  contains  6760  grs. 

1.  How  many  more  grains  does  a  pound  Avoirdupois 
contain  than  a  pound  Troy  ? 

2.  Reduce  8  oz.  12  dwt.  to  pennyweights. 

3.  Reduce  1760  dwt.  to  higher  denominations. 

4.  How  many  grains  are  there  in  an  ounce  of  silver  ? 

5.  From  1  lb.  Troy  take  5  oz.  5  dwt. 

6.  If  1  dwt.  of  silver  is  worth  4  cents,  find  the  value 
of  an  ounce. 

7.  How  many   spoons  weighing  1  oz.  5  dwt.  each 
can  be  made  from  30  oz.  of  silver? 

8.  How  many  table-spoons  weighing  2  oz.  17  dwt. 
each  can  be  made  from  310  oz.  13  dwt.  of  silver  ? 

9.  Divide  373  oz.  2  dwt.  by  7. 

10.  Multiply  27  oz.  13  dwt.  by  6. 

11.  Add  11  oz.  11  dwt.  15  grs. ;  7  oz.  12  dwt.  19  grs. ; 
10  oz.  13  dwt.  17  grs. 

12.  From  7  oz.  19  dwt.  take  3  oz.  19  dwt. 

Note.   Apothecaries,  in  compounding  medicines,  use  the  following : 

Apothecaries'  Measure. 

60  minims  (TT\,)  z=  1  dram  (VCl  Ix.). 
8  drams  =  1  ounce  (fl.  drm.  viij.). 

16  ounces  =  1  pint  (fl.  oz.  xvj.). 


176  LESSON   14. 

TIME    MEASURE. 

Time  Measure  is  used  in  measuring  duration. 

Table. 
60  seconds  (sec.)  =  1  minute  (min.). 

60  minutes  =  1  hour  (hr.). 

24  hours  =  1  day  (dy.). 

7  days  =  1  week  fwk.). 

365  days  (or  52  wks.  1  dy.)  =  1  common  year  (yr.). 

366  days  =  1  leap-year. 
100  years                                =  1  century. 

1.  Reduce  3  dys.  11  hrs.  32  min.  to  minutes. 

2.  Reduce  7  hrs.  30  min.  50  sec.  to  seconds. 

3.  Reduce  20,400  min.  to  higher  denominations. 

4.  Reduce  481,200  sec.  to  higher  denominations. 

5.  From  3  yrs.  15  dys.  take  2  yrs.  12  dys.  23  hrs. 

6.  Divide  10  wks.  5  dys.  9  hrs.  by  9. 

7.  Multiply  2  dys.  7  hrs.  15  min.  by  8. 

8.  From  6  dys.  5  hrs.  48  min.  43  sec.  take  13  hrs. 
30  min.  40  sec. 

9.  Divide  31  dys.  2  hrs.  54  min.  by  7. 

COUNTING. 

Paper.  Various. 

24  sheets     =  1  quire.  12  things  =  1  dozen. 

20  quires     =  1  ream.  12  dozen  =  1  gross. 

2  reams     =  1  bundle.  12  gross    =  1  great  gross. 

5  bundles  =  1  bale.  20  things  =  1  score. 

How  many  sheets  make  a  ream  ? 
How  many  pens  make  a  gross  ? 
How  many  buttons  make  a  great  gross  ? 
How  many  years  are  3  score  and  ten  ? 


LESSON   15. 


177 


LONG    MEASURE. 

Long  Measure  is  used  in  measuring  lines  or  distances. 

Table, 

12  inches  (in.)  =  1  foot  (ft.). 

3  feet  =  1  yard  (yd.). 

5 J  yards,  or  16|  feet  =  1  rod  (rd.). 

320  rods  =  1  mile  (mi.). 

1  mi.  =  320  rds.  =  1760  yds.  =  5280  ft. 

Note.  A  line  =  y^  in.  ;  a  barleycorn  =  J  in. ;  a  hand  (used  in  meas- 
uring the  height  of  horses)  =  4  in.  ;  a  palm  =  3  in, ;  a  span  =  9  in.  ;  a 
cubit  =  18  in.  ;  a  military  pace  =  2^  ft. ;  a  chain  =  4  rds. ;  a  link 
=  j^-Q  chain  ;  a  furlong  =  ^  mi. ;  a  knot  (used  in  navigation)  =  0086  ft.; 
a  league  =  3  knots  ;  a  fathom  (used  in  measuring  depths  at  sea)  =  6  ft. ; 
a  cable  length  =  120  fathoms. 

Note.  Lengths  measured  by  yards  are  generally  expressed  in  yards 
and  fractions  of  a  yard  ;  and  distances  of  100  rds.  and  80  rds.  are 
called  half-miles  and  quarter-miles  respectively. 

Reduce  283  inches  to  higher  denominations. 


12 

283 

3 

23. 

..7 

7. 

..2 

5i 


11 


7  yds.  2  ft.  7  in.  Ans. 

Reduce  328  yards  to  rods. 

Since  it  takes  5^  yards,  or  11  half- 
yards,  to  make  a  rod,  reduce  the  328 
yards  to  half-yards  and  divide  by  11. 
The  quotient  is  69  rods,  and  the  re- 
mainder is  7  half-yards.  The  7  half- 
yards  are  equal  to  Sh  yards. 

59  rds.  3^  yds.  Ans. 


328 

9 


656  half -yards. 
59.  .  .  7  half-yards. 


What  part  of  a  yard 

,Tri  ..^     .  .^  .  „...i 160  rds.  ?   80  rds.*? 


are  9  in.?   18  in. 


vv  11511  part  ui   ct  yitra  a-re 

What  part  of  a  mile  are 

xj^,„  ^ — ,  yards  in  2  rds.?   in  3  rds.?   in  4  rds 
feet  in  2  rds 


How  many  yards 
How  many 


in  2  rds.? 

'^  ^^  4  rds.  ?   in  6  rds.  ? 


m 


178 


LESSON   16. 


1.  Change  5  yds.  2  ft.  7  in.  to  inches. 

2.  Change  2  yds.  2  ft.  4  in.  to  inches. 

3.  Change  2  mi.  268  rds.  to  rods. 

4.  Change  16  mi.  181  rds.  to  rods. 

5.  Change  15,840  ft.  to  miles. 

6.  Change  935  yds.  to  rods. 

7.  Change  720  rds.  to  miles. 

8.  Change  19,360  yds.  to  miles. 
Add: 


yds. 


9. 

ft. 


10. 

yds.         ft. 


13       1       5 

28       2       7 
5       2    11 


27 
14 
14 


4       1 

3       2 
3       2 


12. 

mi. 

ids. 

ft. 

13 

35 

15 

11 

57 

11 

10 

85 

13 

5 

96 

8 

13. 

mi. 

rds. 

ft. 

7 

140 

10 

5 

230 

12 

3 

275 

5 

1 

255 

11 

Find  the  difference  between  : 
15.  16. 

yds.      ft.      in.  yds.     ft.      in. 

14     1     4  22     0     0 

3     15  3     2    6 


18. 

mi.         rds.  ft. 

17     125  1 

8     257  14 


19. 

mi. 

Ids. 

yds. 

7 

0 

0 

3 

255 

1 

21.  Multiply  15  yds.  1  ft.  9  in.  by  11. 

22.  Multiply  21  rds.  4  yds.  2  ft.  by  13. 


11. 

rai.        rds.     yds. 


15     25 

3     27 
12     36 


14. 

rds. 

ft. 

in. 

170 

8 

9 

115 

11 

11 

130 

14 

8 

175 

13 

7 

17. 

mi. 

rds. 

ft. 

23 

76 

1 

16 

238 

15 

20. 

mi. 

rds. 

yds. 

13 

33 

2 

4 

0 

H 

LESSON   17. 


179 


BECT  ANGLE. 


PERIMETERS. 

The  Perimeter  of  any  surface  bounded  by  straight 
lines  is  the  sum  of  the  lengths  of  the  bounding  lines. 

Draw  rectangles  of  the  following  dimensions  and  meas- 
ure their  perimeters : 

2  in.  by  3  in.         2  in.  by  4  in. 

3  in.  by  3  in.         8  in.  by  5  in. 
3  in.  by  4  in.         4  in.  by  6  in. 

Find  the  perimeter  of 

1.  A  rectangular  floor  15  ft.  by  15  ft. 

2.  A  rectangular  ceiling  22  ft.  by  20  ft. 

3.  A  rectangular  room  16  ft.  by  18  ft. 

4.  A  rectangular  room  24  ft.  by  21  ft. 

5.  Find   the    cost   of    fencing   a   rectangular    field 
30  rds.  by  20  rds.,  at  $1.20  a  rod. 

The  length  of  the  circumference  of  a  circle  is  found 
by  multiplying  the  length  of  the 
diameter  by   22  and  dividing  the 
result  by  7. 

Find  the  length  of  the  circum- 
ference of  a  circle  : 

6.  If  the  length  of  the  diameter 
is  21  in. ;  28  in. ;  7  ft. 

The  length  of  the  diameter  of  a  circle  is  found  by 
multiplying  the  length  of  the  circumference  by  7  and 
dividing  the  result  by  22. 

Find  the  length  of  the  diameter  of  a  circle : 

7.  If  the  length  of  the  circumference  is  11  in. 

8.  If  the  length  of  the  circumference  is  2  ft.  9  in. 


180  LESSON   18. 

SQUARE   MEASURE. 

Square  Measure  is  used  in  measuring  surfaces. 
The  units  of  square  measure  are  squares  having  units  of  length 
for  the  lengths  of  their  sides. 

Table. 

144  square  inches  (sq.  in.)=  1  square  foot  (sq.  ft.). 

9  square  feet  =  1  square  yard  (sq.  yd.). 

30|  square  yards,  or  |       ^  ^  ^^^ 

272^  square  feet  J  ^ 


160  square  rods,  or  | 
10  square  chains    / 
640  acres  =  1  square  mile  (sq.  mi.). 


1  acre  (A.) 

1  square  mi 
Hence,  1  A.  =  160  sq.  rds.  =  4840  sq.  yds.  =  43,560  sq.  ft, 


A  square  of  flooring  or  roofing  =  100  sq.  ft. 
A  section  of  land  =  1  mile  square. 

A  township  =  36  sq.  mi. 

The  units  of  square  measure  are  obtained  by  squaring  the  units  of 
long  measure.     Thus, 

144  =  122  ;  9  =  3-2 .  301  =(5^)2  ;  272^  =  (16^)2. 
122  ig  read  the  square  of  12  and  means  12  x  12. 

1.  Reduce  507  sq.  yds.  7  sq.  ft.  to  square  feet. 

2.  Reduce  50  sq.  chains  to  acres. 

3.  Reduce  3  A.  90  sq.  rds.  to  square  rods. 

4.  Reduce  44,996  sq.  in.  to  square  feet. 

5.  Reduce  67,760  sq.  yds.  to  acres. 

6.  Reduce  85,316  sq.  rds.  to  acres. 

7.  Add:  3  A.  116  sq.  rds. ;  2  A.  120  sq.  rds.;  5  A. 
119  sq.  rds. ;  1  A.  40  sq.  rds. 

8.  From  13  sq.  yds.  7  sq.  ft.  12  sq.  in.  take  3  sq.  yds. 
8  sq.  ft.  136  sq.  in. 

9.  Multiply  2  A.  20  sq.  rds.  by  9. 


LESSON   19.  181 

AREAS. 

The  area  of  any  surface  is  the  number  of  units  of  area 
the  given  surface  contains. 

The  unit  of  area  is  a  square,  the  side  of  which  is  some 

given  unit  of  length. 

Find  the  area  of  a  rectangle  2  ft.  3  in.  by  1  ft.  8  in. : 

2  ft.  3  in.  =  24  in.  +  3  in.  =  27  in. 
1  ft.  8  in.  =  12  in.  +  8  in.  =  20  in. 
Therefore  the  area  required  is  20  x  27  =  640  sq.  in. 

Hence,  in  finding  the  area  of  a  rectangle  : 
We  express  the  length  and  breadth  in  units  of  the  same 
denomination.,  and  multiply  the  number  of  units   in  the 
length  by  the  number  of  units  in  the  breadth  ;  this  product 
ivill  be  the  number  of  square  units  of  that  denomination. 

Find  the  area  of  a  rectangle : 

1.  8  in.  by  5  in.      4.  11  in.  by  10  in.      7.  3  ft.  by  2  ft. 

2.  9  in.  by  6  in.      5.  15  in.  by  6  in.        8.  4  ft.  by  2  ft. 

3.  8  in.  by  7  in.      6.  16  in.  by  4  in.        9.  8  ft.  by  2  ft. 

10.  How  many  square  feet  in  a  floor  21  ft.  by  20  ft.  ? 

11.  How  many  square  feet  in  a  floor  18  ft.  by  15  ft.  ? 

12.  How  many   square   feet  in  a   blackboard  12  ft. 
long,  and  3  ft.  wide  ? 

13.  How  many  square  yards  in  a  roll  of  wall-paper 
I  yd.  wide  and  8  yds.  long? 

14.  Find  the  number  of  square  yards  in  a  house-lot 
87  ft.  front  and  102  ft.  deep. 

15.  Find  the  number  of  square  rods  in  a  house-lot 
8  rods  front  and  10  rods  deep. 

16.  Find  the  total  area  of  the  four  ivalls  of  a  room 
18  ft.  long,  15  ft.  wide,  and  9  ft.  high. 


182 


LESSON   20. 


1.  Find  the  total  area  of  the  four  walls  and  the  ceiling 
of  a  room  16  ft.  long,  15  ft.  wide,  and  10  ft.  high. 

2.  Find  the  total  area  in  square  yards  of  the  ceiling  of 
a  room  18  ft.  long,  and  15  ft.  wide. 

3.  Find  the  area  in  square   yards  of   the  four  walls 
of  a  room  19  ft.  long,  17  ft.  wide,  and  9  ft.  high. 

4.  Find  the  number  of  acres  in  a  field  40  rds.  square. 

5.  Find  the  number  of  square  yards  in  a  flower  bed 
that  is  12  ft.  square. 

6.  Find  the  number  of  square  yards  in  a  poppy  bed 
that  is  24  ft.  long,  and  12  ft.  wide. 

7.  Find  the  number  of  square  inches  in  the  surface  of 
a  slate  8  in.  by  14  in. 

8.  Find  the  number  of  square  inches  in  the  surface  of 
a  crayon-box  7  in.  by  4  in.  by  3  in. 

9.  Find  the  number  of  square  feet  in  the  surface  of  a 
cube  3  ft.  by  3  ft.  by  3  ft. 


The  area  of  a  circle  is  found  by  multiplying  the  area  of 
the  square  on  its  radius  by  22  and  dividing  the  result 
by  7. 

Find  the  area  of  a  circle : 

10.  If  the  length  of  the  radius 
is  10  in. ;    16  in. ;    20  in. 

11.  If  the  length  of  the  radius 
is  1  ft.  4  in. ;    1  ft.  6  in. 

12.  If  the  length  of  the  diameter 
is  1  ft.  10  in. ;  2  ft.  4  in. 

13.  If  the  length  of  the  diameter  is  2  ft.  6  in. ;  3  ft. 
4  in.;  3  ft.  8  in.;  3  ft.  10  in. 

14.  If  the  length  of  the  diameter  is  4  ft.  2  in. 


LESSON   21.  183 

CARPETING    FLOORS. 

In  carpeting  floors,  decide  whether  the  strips  shall 
run  lengthwise  of  the  room  or  across  it,  and  find  the 
number  of  strips  required  by  dividing  the  width  of  the 
room  by  the  width  of  the  carpet,  if  the  strips  are  to  run 
lengthwise  of  the  room ;  and  the  length  of  the  room  by 
the  width  of  the  carpet,  if  the  strips  are  to  run  across  it. 
A  fraction  of  a  width  of  carpeting  required  is  reckoned 
a  full  width,  and  enough  is  turned  under  to  make  the 
carpet  fit  the  room. 

The  number  of  yarda  in  the  length  of  the  strip  required 
multiplied  hy  the  number  of  strips  will  give  the  number  of 
yards  of  carpeting  required. 

In  determining  the  length  of  the  strip,  allowance  must 
be  7nadefor  matching  the  patterns. 

Ex.  Find  the  number  of  strips  of  carpeting  27  in. 
wide  required  for  a  rooni  18  ft.  by  17  ft.,  if  the  strips 
run  lengthwise. 

Solution. 
17  ft.  =17  X  12  in.  =  204  in. 
204  in.  -  27  in.  =  7|f. 

Therefore  8  strips  are  required. 

1.  Find  the  number  of  strips  of  carpeting  1  yd.  wide 
required  for  a  room  17  ft.  by  15  ft.,  if  the  strips  run 
lengthwise. 

2.  Find  the  number  of  strips  of  carpeting  27  in.  wide 
required  for  a  room  20  ft.  by  22  ft.  6  in.,  if  the  strips 
run  across  the  room. 

3.  Find  the  number  of  yards  of  carpeting  1  yd.  wide 
required  for  a  room  17  ft.  6  in.  by  17  ft.,  if  the  strips  run 
lengthwise.     What  width  will  be  turned  under  ? 


184  LESSON   22. 

PAPERING    ROOMS. 

Wall-paper  is  made  in  strips  18  in.  wide.  Single  rolls 
are  8  yds.  long,  and  double  rolls  are  16  yds.  long. 

To  find  the  number  of  rolls  required  to  paper  a  room  of 
common  height : 

We  find  the  number  of  feet  in  the  perimeter  of  the  room^ 
omitting  the  width  of  the  doors  and  windows  ;  mid  allow  a 
double  roll^  or  two  single  rolls,  for  every  7  feet  of  the 
perimeter. 

Find  the  number  of  rolls  required  for  a  room  of  ordi- 
nary height,  17  ft.  by  15  ft.,  having  1  door  and  3  windows 
each  4  ft.  wide. 

Perimeter  of  the  room  =  2  x  17  ft.  +  2  x  15  ft.  =  64  ft. 
Width  of  door  and  windows  =  16  ft. 

Deducting,  we  have  48  ft. 

48  -  7  =  6f 

Ans.  7  double  rolls. 

1.  How  many  double  rolls  of  paper  will  be  required 
for  a  room  20  ft.  by  18  ft.,  with  2  doors  and  3  windows, 
each  4  ft.  wide? 

2.  Find  the  cost  of  paper  at  50  cents  a  single  roll  for 
a  room  21  ft.  by  19  ft.,  with  2  doors  and  4  windows,  each 
4  ft.  2  in.  wide. 

3.  Find  the  cost  of  paper  at  30  cents  a  single  roll  for 
a  room  16  ft.  by  15  ft.,  with  1  door  and  2  windows,  each 
4  ft.  wide. 

4.  How  many  double  rolls  of  paper  will  be  required 
for  a  room  the  perimeter  of  which  is  68  ft.,  after  allow- 
ance is  made  for  doors  and  windows  ? 

5.  How  many  double  rolls  of  paper  will  be  required 
for  a  room  the  perimeter  of  which  is  60  ft.,  after  allow- 
ance is  made  for  doors  and  windows  ? 


LESSON   23.  185 

CUBIC    MEASURE. 

Cubic  Measure  is  used  in  measuring  solids. 
The  units  of  cubic  measure  are  cubes  having  units  of  length  for 
the  lengths  of  their  edges. 

Table. 

1728  cubic  inches  (cu.  iii.)=  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 

The  units  of  cubic  measure  are  cubes  of  the  units  of  long  measure. 
Thus,  1728=128;  27  =  S^. 

12^  is  read  the  cube  of  12  and  means  12  x  12  x  12. 

WOOD    MEASURE. 

Table. 

16  cubic  feet  =  1  cord  foot  (cd.  ft.). 
8  cord  feet   =  1  cord  (cd.). 
Therefore,  128  cubic  feet  =  I  cord. 

1.  Reduce  13  cu.  yds.  21  cu.  ft.  to  cubic  feet. 

2.  Reduce  600  cu.  ft.  to  cubic  yards. 

3.  From  58  cu.  yds.  24  cu.   ft.   take   34   cu.   yds. 
26  cu.  ft. 

4.  Multiply  13  cu.  yds.  13  cu.  ft.  by  13. 

5.  Divide  17  cu.  yds.  14  cu.  ft.  by  11. 

6.  Add :  34  cu.  yds.  11  cu.  ft. ;  13  cu.  yds.  10  cu.  ft. ; 

17  cu.  yds.  4  cu.  ft. 

7.  How  many  cords  of  wood  in  1280  cu.  ft.  ? 

8.  How  many  cords  of  wood  in  a  pile  42  ft.  long, 

8  ft.  wide,  and  6  ft.  high  ? 

Note.   Divide  the  product  of  the  numbers!  expressing  the  length, 
width,  and  height  by  128. 

9.  How  many  cubic  yards  in  a  cord  of  wood  ? 

10.    At  $4  a  cord,  find  the  value  of  a  pile  of  wood 

18  ft.  long,  4  ft.  wide,  and  4  ft.  high. 


186 


LESSON  24. 
VOLUMES. 


The  volume  of  any  solid  is  the  number  of  units  of 
volume  the  given  solid  contains. 

The  unit  of  volume  is  a  cube,  the  edge  of  Avhich  is 
some  given  unit  of  length. 

In  finding  the  volume  of  a  rectangular  solid  : 

We  express  the  lengthy  breadth^  and  thickness  in  units 
of  the  same  denomination  ;  then  ive  multiply  the  number 
of  units  in  the  length  by  the  number  of  units  in  the 
breadth^  and  this  product  by  the  number  of  units  in  the 
thickness  ;  the  result  ivill  be  the  yiumber  of  cubic  units  of 
that  denomination. 

Find  the  volume  of  a  rectangular  solid: 

1.  8  in.  X  4  in.  x  3  in.  4.     7  in.  x  3  in.  x  4  in. 

2.  4  in.  X  4  in.  X  3  in.  5.  10  in.  x  8  in.  x  4  in. 

3.  4  in.  X  4  in.  x  4  in.  6.     3  in.  x  3  in.  x  3  in. 

7.  Find  the  number  of  cubic  feet  in  a  stick  of  square 
timber  30  ft.  long,  1  ft.  square  at  the  end. 

8.  Find  the  number  of  cubic  yards  in  an  excavation 
for  a  cellar  42  ft.  by  33  ft.  by  9  ft. 

9.  Find  the  number  of  cubic  yards  in  an  excavation 
for  a  cellar  33  ft.  by  24  ft.  by  9  ft. 


LESSON   25. 
COMMON   FRACTIONS. 


187 


If  a  circle  is  divided  into  2  equal  parts, 

What  part  of  the  whole  circle  is  each  of  these  parts  ? 

What  part  of  the  whole  circle  are  2  of  these  parts  ? 

If  a  circle  is  divided  into  3  equal  parts, 

What  part  of  the  whole  circle  is  each  of  these  parts  ? 
What  part  of  the  whole  circle  are  2  of  these  parts  ? 
What  part  of  the  whole  circle  are  3  of  these  parts  ? 

If  a  circle  is  divided  into  4  equal  parts. 

What  part  of  the  whole  circle  is  each  of  these  parts  ? 
What  part  of  the  whole  circle  are  2  of  these  parts  ? 
What  part  of  the  whole  circle  are  3  of  these  parts  ? 
What  part  of  the  whole  circle  are  4  of  these  parts  ? 
How  many  halves  of  a  unit  make  the  whole  unit  ? 
How  many  thirds  of  a  unit  make  the  whole  unit? 
How  many  fourths  of  a  unit  make  the  whole  unit  ? 

What  is  the  7iame  of  one  of  the  parts  of  a  unit, 

When  the  unit  is  divided  into  two  equal  parts  ? 
When  the  unit  is  divided  into  three  equal  parts  ? 
When  the  unit  is  divided  into  four  equal  parts? 
Which  is  larger  |^  of  a  circle  or  ^  of  the  circle  ? 
Which  is  larger  |-  of  a  circle  or  \  of  the  circle  ? 
Which  is  larger  ^  of  a  circle  or  ^  of  the  circle  ? 


188 


LESSON   26. 


/XVs 

«. 

X 

/  «\ 

/ 

>/s     \ 

Us/ 

Vs 

y^ 

If  a  circle  is  divided  into  5  equal  parts, 
What  part  of  the  circle  is  each  of  these  parts  ? 
What  part  of  the  circle  are  2  of  these  parts?   3  of 
these  parts  ?  4  of  these  parts  ?   5  of  these  parts  ? 

If  a  circle  is  divided  into  6  equal  parts, 

What  part  of  the  circle  is  each  of  these  parts  ? 

What  part  of  the  circle  are  2  of  these  parts  ?   3   of 

these  parts  ?   4  of  these  parts  ?   5  of  these  parts  ?   6  of 

these  parts  ? 

If  a  circle  is  divided  into  8  equal  parts, 

What  part  of  the  circle  is  each  of  these  parts  ? 

What  part  of  the  circle  are  2  of  these  parts  ?   4  of 

these  parts  ?    6  of  these  parts  ?    7  of  these  parts  ?   8  of 

these  parts? 

How  many  Jifths  of  a  unit  make  the  whole  unit  ? 

How  many  sixths  f  how  many  sevenths  ?  how  many 
eighths?  how  many  tenths?  how  many  twelfths?  how 
many  sixteenths? 

What  is  the  name  of  one  of  the  parts  of  a  unit,  when 
the  unit  is  divided  into  5  equal  parts  ?  into  6  equal 
parts  ?  into  8  equal  parts  ?  into  10  equal  parts  ?  into 
12  equal  parts  ? 

Which  is  larger  -I-  of  a  unit  or  J  of  the  unit  ?  |  of  a 
unit  or  J  of  the  unit 


ylg-  of  a  unit  or 


'^:^  of  the  unit. 


LESSON   27.  189 

Any  standard  used  in  counting  or  in  measuring  is 
called  a  unit. 

In  3  quarters  of  a  yard  the  unit  is  a  quarter  of  a  yard. 
But  a  quarter  of  a  yard  is  ii  fractional  part  of  the  whole 
unit,  a  yard. 

A  unit  which  is  a  fractional  part  of  another  unit  is 
called  a  fractional  unit,  and  the  unit  of  which  it  is  a 
part  is  called  its  whole  unit. 

Numbers  that  count  whole  units  are  called  whole 
numbers.  Numbers  that  count  fractional  units  are 
called  fractional  numbers,  or  fractions. 

Note.  The  Teacher  must  explain  tliat  the  words  ichole  and  frac- 
tional^ though  applied  to  numbers,  refer  only  to  the  units  counted  by 
the  numbers. 

Name  the  fractional  unit  and  the  integral  unit  in : 

3  quarters  of  an  inch.  1  half  of  an  hour. 

4  fifths  of  a  pound.  6  sevenths  of  a  week. 

2  thirds  of  a  yard.  5  twelfths  of  a  foot. 

3  eighths  of  a  bushel.  3  sixteenths  of  a  ton. 
9  tenths  of  a  dollar.                   5  sixths  of  an  acre. 

Express: 

J  of  a  yard  in  inches.  \  of  a  pound  in  ounces. 

I  of  a  yard  in  inches.  f  of  a  pound  in  ounces. 

I  of  a  yard  in  inches.  |  of  a  pound  in  ounces. 

I  of  a  yard  in  inches.  |  of  a  pound  in  ounces. 

Every  common  fraction  is  written  in  figures  by  means 
of  two  whole  numbers,  which  are  called  the  terms  of 
the  fraction. 

One  of  these  gives  the  name  of  the  parts,  and  is  called 
the  denominator ;  and  the  other  gives  the  number  of  the 
parts  taken,  and  is  called  the  numerator. 


190 


LESSON   28. 


To  write  a  common  fraction,  write  the  denominator 
under  the  numerator  with  a  line  between  them. 

To  write  5  sevPMths,  for  example,  we  write  the  numerator  5,  draw  a 
line  under  it,  and  under  the  line  we  write  the  denominator  7  ;  thus,  f. 

To  read  a  common  fraction,  read  the  numerator  and 
then  the  denominator. 

Thus,  I,  i,  f,  I,  y\,   are  read  two-thirds,  one-half,   three-fifths, 
seven-eighths,  nine- elevenths,    f  is  read  three-fourths  or  three-quarters. 


seven  twentieths, 
thirteen  twenty-fifths, 
five  sevenths, 
nine  thirteenths, 
eleven  twelfths, 
four  twenty-firsts, 
seventeen  eighteenths, 
thirty  thirty-seconds. 
thirteen  twenty-fourths, 
fifteen  nineteenths. 


Write  in  figures  : 

one  third, 
one  quarter, 
two  fifths, 
five  sixths, 
five  eighths, 
seven  twelfths, 
three  sixteenths, 
nine  fourteenths, 
nine  twentieths, 
four  twenty-fifths. 

RpflH  •      3        5        411_9         3         4        121911 

iteaa.    g,   ^g,   g,  2t^  22'  yy   19'  23'  25'  27- 

If  tlie  numerator  is  smaller  than  the  denominator,  the 
fraction  is  called  a  proper  fraction  ;  as  ^. 

If  the  numerator  is  equal  to  the  denominator,  or  greater 
than  the  denominator,  the  fraction  is  called  an  improper 
fraction;  as  |,  i^-. 

A  mixed  number  is  a  whole  number  and  a  fraction ; 
as  5|,  read  five  and  two-sevenths. 

Every  whole  number  may  be  regarded  as  a  fraction 
having  1  for  the  denominator. 

Thus,  8  may  be  written  f . 


LESSON   29.  191 

How  many  halves  of  an  apple  in  2  apples?  in  3 
apples  ?   in  5  apples  ?   in  6  apples  ?   in  8  apples  ? 

How  many  halves  of  an  apple  in  2J  apples  ?  in  3 J 
apples  ?   in  4J  apples  ?   in  b^  apples  ? 

How  many  quarters  of  a  dollar  in  f  2?  in  13?  in  14? 
in|2i?   in.f3i?   in|4|? 

Change  to  improper  fractions  : 


2=j 

2=j 

2=, 

2=r 

2  =  5 

8=. 

3=j 

3  =  5 

3=ir 

3  =  5 

4  =  1 

4  =  5 

4  =  T 

4=^ 

4  =  5 

5  =  2 

5  =  5 

5  =  5 

5=1. 

5  =  5 

6  =  2- 

6  =  5 

6=5 

6  =  r 

6  =  5 

7=j 

7  =  5 

7  =  , 

7  =  T 

7  =  5 

8  =  ,- 

8  =  5 

8  =  5 

8  =  T 

8  =  5 

9=2 

9  =  5 

9  =  5 

9=5 

9  =  5 

2=5 

2=1. 

2  =  TT 

2  =  TJ 

2  =  T5 

3  =  5 

8=8 

3= IT 

3  =  T. 

3  =  T5 

4  =  5 

4  =  5 

4  =  w 

4  =  TJ 

4  =  T5 

6=5 

5=9 

5=„ 

5  =  T^ 

5=15 

6  =  5 

6=9 

6  =  TTr 

6  =  T2 

6=15 

7  =  5 

7  =  9 

7  =  w 

7=TJ 

7  =  T5 

8  =  5 

8=9 

8  =  TT 

8  =  T^ 

8  =  T6 

9  =  5 

9=^ 

9=w 

9  =  T^ 

9  =  T5 

2i  =  j 

H=5 

2f  =  e 

3i  =  5 

1A  =  T^ 

4i  =  f 

3i  =  5 

3*  =  j 

5^  =  5 

2t^  =  TJ 

6i  =  j 

2i  =  T 

6f=T 

2i=» 

1A  =  T5 

71  =  2 

5i  =  T 

34  =  ^ 

21  =  9 

HHt5 

192 


LESSON   30. 


To  change  an  improper  fraction  to  a  whole  or  mixed 
number : 

We  divide  the  numerator  by  the  denominator. 

The  quotient  will  be  a  whole  number  or  a  mixed  number.  If  a 
mixed  number,  the  fractional  part  will  have  for  numerator  the  re- 
mainder of  the  division,  and  for  denominator  the  divisor. 

Change  to  whole  or  mixed  numbers  the  following  : 


1. 

¥• 

7. 

¥■ 

13. 

¥• 

19. 

!§• 

2. 

¥• 

8. 

-¥- 

14. 

¥• 

20. 

U- 

3. 

H- 

9. 

¥• 

15. 

¥• 

21. 

H- 

4. 

¥• 

10. 

¥- 

16. 

¥• 

22. 

fl- 

5. 

¥• 

U. 

V- 

17. 

¥• 

23. 

it- 

6. 

¥• 

12. 

!!• 

18. 

-tl- 

24. 

H- 

To  reduce  a  fraction  to  lower  terms : 

We  divide  both  terms  by  any  number  that  will  divide 
each  term  without  a  remainder. 


Thus  by  dividing  both  terms  of  -f-^  by  2  we  get 


Note.  The  Teacher  must  illustrate  this  example,  and  other  exam- 
ples until  the  pupils  understand  fully  that  the  reduction  of  a  fraction 
to  lower  terms  does  not  alter  its  value. 

Reduce  to  lowest  terms  : 


1. 

«• 

7.  If 

13. 

H- 

19.  If. 

2. 

if 

8-  A- 

14. 

If 

20.  If. 

3. 

w 

9.  IJ. 

15. 

it- 

21.  §f 

4. 

H- 

10.  If. 

16. 

,'h- 

22.  ff. 

5. 

A- 

11-  U- 

17. 

-h%- 

23.  fl- 

6. 

A- 

12.  it. 

18. 

i^- 

24.  ||. 

LESSON   31.  193 

MULTIPLICATION    OF    FRACTIONS. 

If  we  take  |-  of  ^  of  an  apple,  we  have  J  of  an  apple, 
and  if  we  take  |  of  |  of  an  apple,  we  have  |  of  an  apple. 

Note.  The  Teacher  should  illustrate  this  by  actually  dividing  an 
apple  into  quarters  and  then  each  quarter  into  halves. 

That  is,  -^  of  ^=  g,  and  ^  of  |  =  |.     Hence, 

To  multiply  one  fraction  by  another  : 

We  fake  the  product  of  the  mimeratoris  for  the  required 
numerator^  and  of  the  denominators  for  the  denominator. 

Mixed  numbers  and  ivhole  numbers  may  be  written  as 
improper  fractions,  and  thus  brought  under  the  rule. 

The  work  of  multiplying  fractions  may  be  much 
shortened  by  cancellation ;  that  is,  by  first  dividing  out 
every  number  that  is  contained  in  the  numemtor  and 
denominator  without  remainder. 

Find  the  product  of  f ,  2|,  and  3. 

Now  2i  =  Y",  ^^^  ^  iT^^y  ^6  written  f. 
2 

Hence  the  product  is  ^-li-^  =  3  6  =  71 
J  X    5  X  1       ' 

Cancel  the  7  from  the  denominator  and  from  the  14  in  the  numera- 
tor, and  then  multiply  ;  we  have  ^^^,  or  7i. 

1.  I- of    f  =  7.  7.  I  of    1  =  ,.  13.  fof    f  =  ,. 

2.  lof    1  =  5.  8.  iofi|  =  ^3.  14.  I  of    i  =  ^. 

3.  |ofii  =  „-  9.  i  of  14  =  ,-^.  15.  fof-i/=-j. 

4.  iof    f  =  ^.  10.  iofi^  =  „.  16.  fof    1  =  5. 

5.  i  of  ^  =  „.  11.  i  of  if  =  „.  17.  1^  of  H  =  5. 
6-Jofi|=Te.  12.  ioff2  =  j^.  18.  fof^=^. 


194  LESSON   32. 

To  multiply  a  mixed  number  by  a  whole  number  : 

We  multiply  the  fraction  firsts  and  then  the  integral  part 
of  the  mixed  number^  and  add  the  results. 

Find  the  products  of : 

1.  2x2-1.  8.  4x21.  15.  5x21 

2.  2x31-.  9.  4x3J.  16.  5x2|. 

3.  2x3J.  10.  4x2J.  17.  5x3f. 

4.  3x31.  11.  4x31.  18.  5x4|. 

5.  3x21.  12.  4x41.  19.  5xl|. 

6.  3x51.  13.  4x4f  20.  5x2i. 

7.  3x31.  14.  4x3i.  21.  5x 


To  multiply  a  whole  number  by  a  mixed  number : 

We  multiply  the  ivhole  number  hy  the  fraction  firsts  and 
then  hy  the  integral  part  of  the  mixed  number^  and  add 
the  results. 

Multiply  8  by  21 

8 

21 
Here  we  multiply  8  by  i  and  get  2|.  "^ 

Then  we  multiply  8  by  2  and  get  16.  2|^ 

By  adding  the  2f  and  the  16  we  obtain  18f .  16 

Find  the  products  : 

1.  21x6.  6.  21x12.  11.  71x21. 

2.  2^x6.  7.  2|x8.  12.  8|x22. 

3.  3^x6.  8.  2f  x9.  13.  2ix6f 

4.  3Jx6.  9.  3|^x20.  14.  3Jx8f 

5.  41x6.  10.  3|xl2.  15.  3ix6f 


LESSON   33. 


195 


niVISION  OF  FRACTIONS. 

To  divide  |  of  a  dollar  by  ^  of  a  dollar  is  to  find  the 
number  of  quarters  of  a  dollar  it  is  necessary  to  take  in 
order  to  have  half  a  dollar.  It  is  obvious  the  number 
is  2.     Hence, 


hH 


But  1x4 


:2. 

2. 


Therefore,  to  divide  by  \  gives  the  same  result  as  to 
multiply  by  \. 

Now  f  is  J  inverted.     Therefore, 

To  divide  by  a  fraction : 

We  invert  the  fraction  and  multiply. 
Mixed  numbers  and  whole  numbers  may  be  ivritten  as 
improper  fractions.,  and  thus  brought  under  the  rule. 

Find  the  quotients : 


2.  1^1 

3 

4 

8.  6-1 

9.  1^6. 


9    •    3 
3    •    9 


13.  2  H-2J. 

14.  2  -3J. 

15.  %\-^2. 

16.  31-3. 

17.  2^-3. 

18.  51^7. 

19.  2|-4. 


25.  ^^^. 

26.  ^-^^. 

27.  2^-41. 

28.  ^^^. 

29.  81^41. 

30.  41       ^ 

31.  81  ^1|. 


20.  4 


^31 


32.  b\ 


10.  #H- 


li- 


11.  I^f. 


12.  I 


21.  6  -^ll. 

22.  4  -2f 

23.  4  -11 

24.  8  -2-|. 


33.  4|h-31 

34.  5J^2f. 

35.  2|-5J. 

36.  71^  If 


If- 


196  LESSON  34. 

SIMIL.AK    FKACTIONS. 

If  both  terms  of  a  fraction  are  multiplied  by  the  same 

number,  the  value  of  the  fraction  is  not  altered. 

By  this  operation  the  number  of  parts  is  increased,  and  the  size  of 
the  parts  is  decreased,  at  the  same  rate. 

Fractions  that  have  a  common  denominator  are  called 
similar  fractions. 

Reduce  |-,  |,  |-  to  similar  fractions,  having  12  for  their 
common  denominator. 

We  find  the  required  numerators  by  dividing  12  by  the  denom- 
inator of  the  first  fraction  and  multiplying  the  result  by  the  numerator 
of  the  first  fraction  ;  and  so  proceed  with  each  of  the  given  fractions. 
Thus, 

12  -  2  =  6,  and  1  x(S  =  Q.     Therefore  \  =  j% 

12  --  3  =  4,  and  2  X  4  =  8.     Therefore  |  =  y^. 

12  -  4  =  3,  and  3x3  =  9.     Therefore  |  =  j%. 

Hence  the  required  fractions  are  j%,  j%,  j%.     Therefore, 

To  reduce  fractions  to  similar  fractions  with  a  given 
common  denominator : 

We  divide  the  given  common  denominator  hy  the  denoin- 
inator  of  the  first  fraction^  and  multiply  the  quotient  hy  its 
numerator^  and  this  will  he  the  required  numerator  of  the 
first  fraction.  In  the  same  way  we  find  the  numerator  of 
each  of  the  other  fractions. 

Reduce  to  similar  fractions  having  for  denominator 
the  number  given  in  parenthesis  for  each  problem : 


1-  h  f-  1  (12). 

6.  f,  I,  A  (24). 

11.  f,  f,  A  (24). 

2.  i,  1  Vj  (12). 

7. 1-,  f,  Jj  (14). 

12.  f,  W,  f  (28). 

3.  i,  1, 1  (18). 

8.  i,  f  ^T  (21). 

13-  A'  A-  1  (36). 

4-  h  f'  f  (8)- 

9-  h  h  ^z  (15)- 

14.  f,  {^,  ^j  (42). 

5.  J,  f,  Jj  (18). 

10.  ^,  f,  ^  (42). 

15.  !,  1^,  A  (75). 

LESSON   35.  197 

ADDITION    OF    FRACTIONS. 

Add  1,  J,  f . 

These  fractious  changed  to  similar  fractions  with  denominator  12 
become  ^^,  ^^,  j%,  and  ^^  +  /j  +  j%  =  if. 
But  }f  =  f  =  1^.     Therefore, 

To  add  fractions : 

We  change  the  fractions  to  similar  fractions  (if  they 
are  not  similar)^  and  write  the  sum  of  the  nujnerators  of 
the  similar  fractions  over  the  commo7i  denojninator. 

We  reduce  the  resulting  fraction  to  its  lowest  terms  ; 
and  if  it  is  an  improper  fraction^  ive  reduce  it  to  a  whole 
or  mixed  number.  * 

Change  to  similar  fractions  and  add : 


i+\=i 

i+    \  = 

=  12 

i  + 

1 

6 

=  1^ 

i 

+ 

i=TJ 

Hi=i 

H  i= 

=  2^ 

i  + 

i 

=  ^ 

i 

+ 

A  =  l^ 

|-  +  i=c 

H  i  = 

'6 

i  + 

iV 

=  2^ 

i 

+ 

i=.T 

i  +  i=6- 

HtV= 

=  12 

i  + 

tV 

=  12 

i 

+ 

4=Tf 

f+Hw 

i+  i= 

=  20 

i  + 

1^ 

=  T6 

i 

+ 

i=j? 

1=6 

i=8 

2  =  10 

2=r2 

"2  =  12 

i=6 

i  =  ^ 

i  =  TO 

Ht5 

i  =  TJ 

J  =  ^ 

i  =  ^ 

tV  =  to 

tV  =  T2" 

lV  =  T2 

i  =  W 

i  =  T2 

i  =  12" 

i=i8- 

i  =  TJ 

i  =  T6 

i  =  T2 

6=T2 

6  =  l¥ 

i  =  TJ 

tV  =  T6 

T2=T2 

'12=J2_ 

i  =  T8 

Ht. 

2  =  12 

i  =  T2 

2  =  2T 

6=2T 

6=^ 

i  =  T2 

i  =  T2 

4=2T 

i  =  2¥ 

9  =  ¥6 

9=12 

6=12 

i=2¥ 

tV=2¥ 

¥=36 

198  LESSON   36. 

SUBTKACTION   OF    FRACTIONS. 

Subtract  ^  from  |. 

These  fractions  changed  to  similar  fractions  having  12  for  a 
denominator  become  y\,  j%  ;  and  j%  -  ^^  =j\.     Hence, 

To  subtract  one  fraction  from  another : 

We  change  the  fractio7is  to  shnilar  fractions  (if  they 
are  not  similar^ ;  then  subtract  the  numerator  of  the 
subtrahend  from  that  of  the  miyiuend^  and  write  the 
reynainder  over  the  common  denominator. 

We  reduce  the  resulting  fraction  to  its  lowest  terms. 

Change  to  similar  fractions  and  subtract : 

2~J  2~8  2~6  2~6  3~6 

1=-^  1—-  1—-.  1  — „  1_ 

i      J  8~8  6~6  3~"6  6  ""6 


i—^  3— T2  i— T^  i— 12  |  — ¥ 

1__  1  — 1__  _1    _     _  1_ 

9~9  4~]2  5~15  12~~12  2~¥ 


2. j5 3 4 4 

3~6  8~"^  5  "10  5—10  5  —  20 

1— _  1  — _  _1_ 1— 3_     _ 

2"~6  2"~¥  2~10  2~]0  4"~20 


*= 

TJ 

i= 

■TJ 

1= 

^¥ 

i= 

'S 

1= 

ITS 

A= 

To 

A= 

I7f 

1= 

10 

i= 

16 

■ts  = 

'16 

3_  ^_  

4  —  20  5—10  2—10  "5—10 

5  — 2"0  To"  ^10"  5^10"  T0"^TO 


iV—  10  /o  —  10  16  —  16  16  —  11 

10"  5—  1"0  ^~16  4— Ti 


1_ 1_ 3__  5___ 

It  ~  16  2  ~  1 6  ?  —  1 2  6  ~"  1 2 

1%  =  T6  T6  — 16  T2— T5^  ?— 12 


i= 

T^ 

1  _ 

'5  — 

15 

3_ 

5~ 

TO 

-h= 

TO 

1  = 

TO 

2_ 
5  — 

TO 

il  = 

T6 

1- 

T6 

1  = 

T2 

^^2  = 

12 

tV= 

TO 

2  _ 

5  ~ 

10 

3_ 
4  — 

T2 

1  = 

T2 

i= 

12 

«= 

12 

LESSON   37.  199 

CONVERSION    OF    FRACTIONS. 

A  decimal  fraction  is  a  common  fraction  whose  de- 
nominator is  one  of  the  numbers  10,  100,  1000,  etc. 
Thus,  0.4  is  the  same  as  y^j. 

To  convert  a  decimal  fraction  to  a  common  fraction : 

We  take  for  the  numerator  the  entire  number  obtained 
after  removing  the  decimal  poirit^  and  for  the  denominator^ 
1  followed  by  as  ma7iy  zeros  as  there  are  decimal  places 
in  the  original  fraction  ;  and  reduce  the  resulting  fraction 
to  its  loivest  terms. 

Thus,  3.25  =  fe  =  ¥  =  31- 

To  convert  a  common  fraction  to  a  decimal  fraction : 
We  divide  the  numerator  by  the  denominator. 

Thus,  ^  =  i-|ftft  =  0.125. 

4  ^  ^oM.  =  0.571f . 
1=2.00    =o.()66f. 

Note.  If  the  division  does  not  terminate  at  the  third  decimal  place, 
three  decimal  places  will  be  sufficiently  accurate  for  most  problems. 
If  the  number  at  the  fourth  decimal  place  is  gi-eater  than  5,  we  add  1 
to  the  third  decimal  figure;  if  it  is  equal  to  5,  we  cany  the  decimal 
to  four  places.    Thus,  f  =  0.571,  |  =  0.667,  and  ^  =  0.4376. 

Change  to  common  fractions  : 


1.    0.08. 

4.    0.375.           7. 

0.425. 

10. 

3.125. 

2.   0.625. 

5.    0.004.           8. 

0.015. 

11. 

1.725. 

3.   0.032. 

6.    0.256.           9. 

7.075. 

12. 

7.875. 

Change 

to  decimal  fractions : 

13.  -h^ 

14.  A. 

15.  iV 

16.  ^V-               19. 

17.  2%-             20. 

18.  ^,.             21. 

17f 

5|. 

22. 
23. 

24. 

200  LESSON   38. 

ORAL    EXERCISES. 

1.  How  many  inches  in  f  of  a  yard  ? 

2.  How  many  ounces  in  |  of  a  pound  ? 

3.  How  many  pounds  in  J  of  a  ton  ? 

4.  How  many  cubic  feet  in  |  of  a  cubic  yai'd? 

5.  How  many  square  rods  in  |^  of  an  acre  ? 

6.  How  many  cord  feet  in  |^  of  a  cord  ? 

7.  How  mau}^  pints  in  y^g  of  a  gallon? 

8.  How  many  hours  in  J  of  a  day  ? 

9.  How  many  minutes  in  |^  of  an  hour  ? 

10.  How  many  quarters  of  a  pound  in  2  pounds? 

11.  How  many  quarters  of  a  dollar  in  f  6|?  in  $7^7 

12.  How  many  halves  of  an  apple  in  4 J  apples  ? 

13.  I  have  a  string  2|  yards  long.    Into  how  many 
pieces,  each  ^  yard  long,  can  I  cut  it  ? 

14.  How  many  gallons  will  10  bottles  hold  if  each 
bottle  holds  |-  of  a  gallon? 

15.  Find  the  price  of  2^  dozen  of  eggs  at  16  cents  a 
dozen. 

16.  Find  the  price  of  3J  pounds  of  sugar  at  6  cents  a 
pound. 

17.  How  many  miles  will  a  man  walk  in  2  hours  at 
the  rate  of  S^  miles  an  hour  ? 

18.  How  many  miles  will  a  man  walk  in  2|  hours  at 
the  rate  of  3  miles  an  hour  ? 

19.  How  many  miles  will  a  man  walk  in  3  hours  at 
the  rate  of  3  J  miles  an  hour  ? 

20.  Express  2  ft.  6  in.  as  the  fraction  of  a  yard. 

21.  At  $7  a  ton  what  is  the  cost  of  |^  of  a  ton  of  coal  ? 

22.  At  16  a  cord  what  is  the  cost  of  |^  of  a  cord  of 
wood  ? 

23.  At  80  cents  a  bushel  what  is  the  cost  of  2|  bushels 
of  Baldwin  apples  ? 


LESSON   39.  201. 

SLATE    EXEKCISES. 

Find  the  cost,  reckoning  every  fraction  of  a  cent  as  a 
cent : 

1.  3|  doz.  of  eggs  at  24  cents  a  dozen. 

2.  3J  lbs.  of  steak  at  23  cents  a  pound. 

3.  2J  lbs.  of  tea  at  Q5  cents  a  pound. 

4.  17|  yds.  of  muslin  at  10  cents  a  yard. 

5.  50  cans  of  tomatoes  at  $1.25  a  dozen. 

6.  2|  bu.  of  potatoes  at  18  cents  a  peck. 

7.  16  bu.  of  oats  at  37J  cents  a  bushel. 

8.  24  bags  of  corn  at  f  1.12i-  a  bag. 

9.  36  bu.  of  wheat  at  S1^  cents  a  bushel. 

10.  4  lbs.  and  12  oz.  of  butter  at  20  cents  a  pound. 

11.  8  lbs.  and  10  oz.  of  mutton  at  12  cents  a  pound. 

12.  6  qts.  of  molasses  at  56  cents  a  gallon. 

13.  43^  yds.  of  cotton  cloth  at  7  cents  a  yard. 

14.  14  lbs.  6  oz.  of  ham  at  14  cents  a  pound. 

15.  6  bu.  and  3  pks.  of  wheat  at  92  cents  a  bushel. 

16.  2680  lbs.  of  hay  at  122  a  ton. 

17.  2  t.  8  cwt.  of  coal  at  15.60  a  ton. 

18.  31  bbls.  of  flour  at  15.50  a  barrel. 

19.  2|  bu.  of  cranberries  at  7  cents  a  quart. 

20.  3  pks.  and  4  qts.  of  cranberries  at  $  2.56  a  bushel. 

21.  2  cds.  and  6  cu.  ft.  of  wood  at  $3.50  a  cord. 

22.  A  pile  of  wood  26  ft.  long,  4  ft.  wide,  and  5  ft. 
high  at  $3.84  a  cord. 

23.  4  doz.  and  8  eggs  at  30  cents  a  dozen. 

24.  75000  bricks  at  $6.75  a  thousand. 

25.  9  shares  of  stock  at  $  98^  a  share. 


202  LESSON  40. 

BILLS. 

A  Bill  of  Goods  is  a  written  statement  of  g^oods 
sold,  and  of  payments,  if  any,  received  for  them. 

A  Bill  of  Services  is  a  written  statement  of  ser- 
vices rendered,  or  of  labor  performed. 

A  Statement  of  Account  is  a  statement  of  the  sum 
due  according  to  the  accounts  already  rendered. 
Thus, 


Tliv.  Jcyn^, 


To   BROWN    &    CO.,  Dr. 


June,  1    To  Account  rendered 


The  Creditor  is  the  person  who  sells  the  goods, 
or  who  performs  the  labor. 

The  Debtor  is  the  person  who  buys  the  goods,  or 
who  pays  for  the  services  rendered. 

The  Debit  Side  of  the  Account  consists  of  the 
items  due  to  the  person  who  renders  the  account. 

The  Credit  Side  consists  of  the  amounts  received 
by  the  person  who  renders  the  account. 

The  Balance  of  an  Account  is  the  difference  be- 
tween the  amounts  of  the  Debit  and  Credit  Sides. 

Note.  When  a  bill  is  paid,  it  should  be  receipted  by  writing  at  the 
bottom  of  the  bill  the  date  of  payment  and  the  words  Beceived  pay- 
ment, and  under  these  words  the  creditor  should  sign  his  name  and 
deliver  the  receipt  to  the  debtor. 

If  a  clerk  has  authority  to  sign  his  employer's 
name,  he  should  write  under  his  employer's  name 
his  own  name  preceded  by  the  word  by  or  per. 


LESSON   41.  203 

RECEIPTED  BILLS  OF  GOODS. 

Boston^  June  i,  1893. 

nil.  f^alytit  ^Axyymaru, 

Bought  of  CHARLES    EDMONDS. 


1893 
May 

15 

10  lbs.  Coffee 

@35^  1 

$3 

50 

50  lbs.  Sugar 

@    5^  1 

^ 

50 

2  lbs.  Tea 

@65^ 

1 

30 

28  lbs.  Butter 

@32^ 

8 
16 

96 
26 

June  1,  1893.  Received  payment, 


JdTyib^  ycyiA, 


Exeter.,  June  1,  1893. 
To  KELLY  &  GARDNER.  Dr. 


1893 

Mar. 

8 

To  2  gals.  Molasses  @        55^ 

$1 

10 

$ 

To  2  bbls.  of  Flour  @  $5.75 

11 

50 

12 

60 

Apr. 

5 

To  15  lbs.  Rice           @          9^ 

1 

35 

To  25  lbs.  Butter       @        33^       8 

25 

9 

60 

22 

20 

Cr. 

Mar. 

8 

By  2  cords  Birches    @  $4.50<^ 

9 

00 

By  3  bu.  Potatoes      @        65^ 
Balance  due 

1 

95 

10 

95 

11 

25 

June  1, 1893.  Received  payment, 


204 


LESSON   42. 


Make  out  bills,  and  receipt  for  them  the  first  day 
of  the  month  that  follows  the  purchase  : 

Bought  of  JOHN  THOMPSON   &  CO. 


1893 

Feb. 

7 

'is 

9  lbs.  Ham 
18  "    Steak 
15  "    Mutton 
11   "     Veal 

@15P 
@25p 
@16^ 

2.  jci7ybt'3i.  ^(yffimy, 


To  HOWARD  MANSUR,   Dr 


1898 
May 

8 

25  lbs.  Codfish 

@       9^ 

ii 

10 

30   "    Bacon 

@     10 

i( 

18 

10   "    Coffee 

@     85^ 

" 

25 

2  bbls.  Flour 

@  $5.75 

I.  fa/b'Tb  '/Tldv^AycM, 


To  ROBERT  STUART,   Dr. 


1898 

Mar. 

8 

12  doz.  Eggs 
17  lbs.  Butter 

@26^ 
®32^ 

a 

15 

34    ''    Cheese 
16  bu.  Potatoes 

@    8p 
@85fi 

1898 



Apr. 

5 

27  bags  Whole  Com 
80    "     Meal 

@  $1.12 
(S    1^00 

(( 

12 

60    "      Oats 
7  tons  Hay 

@    0.65 
@  17.00 

(( 

19 

Cr. 
By  Cash 

$200 

LESSON   43.  205 

PERCENTAGE. 

A  percentage  of  a  number  is  the  result  obtained  by 
taking  a  stated  number  of  hundredths  of  it. 

One  hundredth  of  a  number  is  called  one  per  cent  of 
it ;  two  hundredths,  two  per  cent ;  three  hundredths, 
three  per  cent ;  and  so  on. 

This  sign  %  stands  for  the  words  per  cent. 

Thus,    5    %  of  300  means  0.05    of  300. 

15^  %  of  300  means  0.15i  of  300. 

\  %  of  300  means  0.00^  of  300. 

When  the  per  cent  can  be  expressed  a.s  a  common  fraction  in  small 
terms^  it  is  better  to  write  it  as  a  common  fraction. 

50  1 

50  %  of  a  number  is  or    -  the  number. 

^°  100  2 

25  1 

25  %  of  a  number  is  —  or     -  the  number. 
'"  100  4 

75  %  of  a  number  is  — ^  or    -  the  number. 
'"  100  4 

12.^  1 

12  il  %  of  a  number  is  — 2  or    -  the  number. 

-  '"  100  8 

gi  1 

8i%  of  a  number  is  -^  or  —  tlie  number. 

^  ^"  100        12 


16|%of  anumber  is 

100 

-  the  number. 

33i%of  anumber  is 

100 

-  the  number. 
3 

66f  %  of  a  number  is 

100 

2 

-  the  number, 

3 

20  %    of  a  number  is 

2«    or 
100 

-,the  number. 
5 

125  %  of  a  number  is 

125  or 
100 

-  the  number. 
4 

Express  as  per  cent : 

i 

i     -h     i 

5 
6 

f      A 

i 

i     i     1- 

i 

f      iV 

206 


LESSON   44. 


Find  161%  of  336. 


336 

0.16J 

112 

2016 

336 

54.88 


16i%  =  0.16^. 


Find  16|%  of  336. 

16|%  =  i 
I  of  336  =  56. 

^Q.  Ans. 
Hence, 


54.88.  A71S. 
To  find  a  per  cent  of  a  number  : 
We  multiply  the  number  by  the  given  per  cent. 
Find  : 


1. 

6%  of  175. 

6. 

331%  of  1840. 

2. 

25%  of  300. 

7. 

50%  of  1216  oz. 

3. 

16|%  of  480  men. 

8. 

66f  %  of  1518  lbs 

4. 

51%  of  675  sheep. 

9. 

75%  of  2040  ft. 

5. 

10%  of  1560dys. 

10. 

121%  of  1648  mi. 

To  find  the  per  cent  one  given  number  is  of  another. 
What  per  cent  of  9  is  3  ? 


Since  1  is  i  of  9,  3  is  3  x  i 


1  =  1;  and  i  =  3)1.00 

0.331  ^  3310/^. 


The  same  result  is  obtained  if  we  divide  3  by  9.     9)3.00 

0.333 


331%. 


Hence, 

To  find  the  per  cent  one  number  is  of  another  : 

We  divide  the  number  which  represents  the  percentage 
by  the  other  number^  carrying  the  division  to  hundredths. 

What  per  cent  of 


1.  90  is  30? 

2.  960  is  24? 

3.  30  is  90? 

4.  24  is  960? 

5.  4108.5  is  821.7? 


6.  2740  mi.  are  548  mi.  ? 

7.  36  in.  are  27  in.  ? 

8.  12.75  are  10.35? 

9.  2240  lbs.  are  2000  lbs.  ? 
10.  7000  grs.  are  5760  grs.  ? 


LESSON   45.  207 

INTEREST. 

Money  paid  for  the  use  of  money  is  called  Interest. 
The  money  at  interest  is  called  the  Principal. 
The  sum  of  the  interest  and  principal  is  called  the 
Amount. 

To  find  interest  for  a  given  number  of  months  at  6%  : 

We  put  the  decimal  point  two  places  to  the  left  in  the 
principal,  and  multiply  by  one-half  the  number  of  months. 

Find  the  interest  on  $630  for  4  mos.  at  6% : 

S6  30 

Q  Here  we  put  the  decimal  point  tico  places  to  the  left  in 

— — — -     the  principal,  and  multiply  by  2  ;  that  is,  by  \  of  4. 

If  we  wished  to  find  the  interest  at  4J%,  we  should 
divide  the  $12.60  by  6,  and  multiply  the  quotient  by  ^^. 

Find  the  interest  on  : 

1.  $1220.40for  3  mos.  at  6%. 

2.  $2612.80for  4mos.  at5%. 

3.  $2084.20  for  1  mo.  at  ^%. 

4.  $4500.60  for  5  mos.  at  5|%. 

5.  $7508.50  for  6  mos.  at  31%. 

6.  $8501.20  for  3  mos.  at  5%. 

7.  $9056.75  for  7  mos.  at  6%. 

To  find  the  amount : 

We  find  the  interest  and  add  it  to  the  principal. 

Find  the  amount  of  : 

8.  $1000  for  4  mos.  at  6%. 

9.  $1500  for  6  mos.  at  4%. 
10.   $75.50  for  4  mos.  at  5%. 


208  LESSON   46. 

To  find  interest  for  a  given  number  of  days  at  6%  : 

We  put  the  decimal  point  three  places  to  the  left  in  the 
principal^  and  multiply  hy  one-sixth  of  the  number  of  days. 

Find  the  interest  on  17260  for  90  dys.  at  6%. 

$  7.260  Here  we  i)ut  the  decimal  point  three  places  to  the 

15         left  in  the  principal,  and  multiply  by  15  ;  that  is,  by  \ 

1108.900     ^f  ^0. 

To  find  the  interest  for  any  other  rate  than  6  per  cent : 
We  find  the  interest  at  Q  %^  divide  the  result  hy  6,  a^id 

multiply  the  quotient  hy  the  given  rate. 

If  the  time  is  given  in  months  and  days ;  or  in  years, 
months,  and  days ;  reduce  the  time  to  days,  reckoning 
30  days  for  a  month,  and  360  days  for  a  year. 

Find  the  interest  on : 

1.  13600  for  30  dys.  at  6%. 

2.  $4500  for  33  dys.  at  6%. 

3.  $8000  for  93  dys.  at  6%. 

4.  $9875  for  60  dys.  at  5%. 

5.  $2525  for  63  dys.  at  ^%. 

6.  $3750  for  90  dys.  at  31%. 

7.  $15.80  for  63  dys.  at  4%. 

8.  $256.40for  45  dys.  at5i%. 

9.  $645.25for  123  dys.  at  3%. 

10.  $950.50  for  2  yrs.  4  mos.  6  dys.  at  6%. 

11.  $20,000  for  1  yr.  7  mos.  at  4%. 

12.  $515.25  for  1  yr.  9  mos.  8  dys.  at  ^%. 

13.  $1000  for  2  yrs.  1  mo.  19  dys.  at  5%. 

14.  $216.75  for  2  yrs.  2  mos.  21  dys.  at  5i%. 

15.  $927.35for  lyr.  8  mos.  28dys.  at3%. 


ANSWERS. 


Lesson  36.  Page  145. 

1.  1102. 

7.  1447.      13.  133.77. 

19.  438,997. 

2.  1445. 

8.  14,219.     14.  222,038. 

20.  527.4053. 

3.  1982. 

9.  18,078.     15.  209,381. 

21.  171.8762. 

4.  986. 

10.  26,405.     16.  260.164. 

22.  200.8964. 

5.  1712. 

11.  25,934.     17.  72.4347. 

23.  85.351. 

6.  1283. 

12.  231.84.     18.  $636.43. 
Lesson  37.  Page  146. 

24.  1491.4375. 

25.  $194.36. 

1.  $18,214. 

3.  2,480,195.    5.  1,602,778. 

7.  1,019,007. 

2.  2017. 

4.  1,638,162.    6.  1,471,784. 
Lesson  38.  Page  147. 

8.  711,998. 

1.  704. 

6.  1921.      11.  11,878. 

16.  116,689. 

2.  381. 

7.  3868.      12.  2795. 

17.  457,547. 

3.  523. 

8.  350.       13.  10,748. 

18.  41,799. 

4.  42(3. 

9.  2529.      14.  8757. 

19.  85,216. 

5.  159. 

10.  1310.      15.  31,407. 
Lesson  39.  Page  148. 

20.  24,184. 

1.  0.06. 

9.  5.855.      17.  18.7132. 

24.  33.151. 

2.  0.78. 

10.  2.759.      18.  5.8908. 

25.  0.0023. 

3.  0.893. 

11.  0.668.      19.  1.0276. 

26.  747.8268. 

4.  2.306. 

12.  1.857.      20.  0.9558. 

27.  761.613. 

5.  0.067. 

13.  0.885.      21.  2.475. 

28.  18.777. 

6.  0.107. 

14.  0.072.      22.  74.2425. 

29.  57.6246. 

7.  2.224. 

15.  0.505.      23.  0.5176. 

30.  5.8435. 

8.  0.882. 

16.  3.1989. 

Lesson  40.  Page  149. 

1.  52. 

4.  1106.       7.  71,041. 

10.  51. 

2.  m. 

5.  2920.       8.  109,008. 

11.  $1.17. 

3.  1782. 

6.  76,831.      9.  14,095. 
Lesson  41.  Page  160. 

1.  7374. 

5.  9765.       9.  34,260. 

13.  26,394. 

2.  9566. 

6.  14,245.      10.  8256. 

14.  16,394. 

3.  8637. 

7.  14,268.     11.  33,882. 

15.  34,584. 

4.  10,971. 

8.  10,344.     12.  18,744. 
209 

16.  46,935. 

210 

ANSWERS. 

17.  31,304. 

26.   15,138. 

35.   117,416. 

44. 

206,712. 

18.  41,335. 

27.  49,445. 

36.  352,640. 

45, 

,  688,275. 

19.  40,524. 

28.  35,908. 

37.  340,278. 

46. 

508,624. 

20.  54,978. 

29.  58,668. 

38.  220,969. 

47. 

607,401. 

21.  65,688. 

30.  27,153. 

39.  300,656. 

48. 

,  270,879. 

22.  34,696. 

31.  30,195. 

40.  504,126. 

49. 

438,921. 

23.  29,355. 

32.  53,400. 

41.  312,741. 

50. 

399,063. 

24.  26,082. 

33.  60,501. 

42.  332,343. 

51. 

798,384. 

25.  16,338. 

34.  61,686. 

Lesson  42 

43.  658,674. 
.    Page  151. 

1.  3648. 

9.  27,553. 

17.  4,235,374. 

25. 

4,175,712. 

2.  8512. 

10.  69,184. 

18.  5,952,816. 

26. 

0,418,652. 

3.  20,440. 

11.  34,272. 

19.  5,921,580. 

27. 

3,412,836. 

4.  8556. 

12.  56,066. 

20.  4,212,032. 

28. 

5,356,521. 

5.  18,112. 

13.  72,412. 

21.  1,601,613. 

29. 

3,276,303. 

6.  26,508. 

14.  47,058. 

22.  786,714. 

30. 

6,731,472. 

7.  14,763. 

15.  62,568. 

23.  4,533,573. 

8.  20,444. 

16.  3,566,541. 

24.  2,722,225. 

Lesson  43, 

,    Page  152. 

» 

1.  4670. 

8.  101,088,000.             15. 

11,428,368,000. 

2.  31,200. 

9.  194,880,000.              16. 

172,437,740,000. 

3.  587,000. 

10.  350,420,000.              17. 

10,800. 

4.  18,-336,000. 

11.  104,832,000.              18. 

48,000. 

5.  29,124,000. 

12.  97,290,000.                19. 

108,000. 

6.  40,635,000. 

13.  50,430,400.               20. 

$210, 

7.  86,140,000. 

14.  49,854,240. 

Lesson  44 

.    Page  153. 

1.  240.204. 

7.  6601.68. 

13.  11.9385. 

19. 

6828.467. 

2.  197.896. 

8.  5165.71. 

14.  91.008. 

20. 

54.2913. 

3.  1769.08. 

9.  436.5. 

15.  101.1725. 

21. 

25.6275. 

4.  55.5676. 

10.  0.8421. 

16.  21015.984. 

22. 

87.0672. 

5.  367,848. 

11.  34.704. 

17.  3417. 

23. 

4603.8601. 

6.  232.379. 

12.  0.0164. 

Lesson  45, 

18.  9550. 
Page  154. 

24. 

4954.6497. 

1.  109,500. 

4.  $97.75. 

7.  1140. 

10. 

14,560  ft. 

2.  57,096. 

5.  .$66.50. 

8.  $567. 

11. 

$32.40. 

3.  .$67.20. 

6.  .$999. 

Lesson  49, 

£.  354.36. 
Page  158. 

1.  217. 

5.  36. 

9.  54. 

13. 

113. 

2.  292. 

6.   143. 

10.  117. 

14. 

105. 

3.  149. 

7.  175. 

11.  121. 

15. 

69. 

4.  108. 

8.   103. 

12.  115. 

16. 

256-1. 

ANSWERS. 

S 

17. 

235-2. 

30. 

327. 

43. 

3250-3. 

56. 

27,873-2. 

18. 

211-1. 

31. 

1855-1. 

44. 

979-4. 

57. 

14,353-5. 

19. 

180-1. 

32. 

1075-1. 

45. 

47,937. 

58. 

4290-2. 

20. 

143-4. 

33. 

2116-3. 

46. 

15,291. 

59. 

1769-3. 

21. 

124-4. 

34. 

1914-3. 

47. 

11,693. 

60. 

6260. 

22. 

100-7. 

35. 

1163-5. 

48. 

15,659. 

61. 

9341. 

23. 

2897. 

36. 

1237. 

49. 

11,062. 

62. 

15,085-4. 

24. 

1958. 

37. 

541-1. 

50. 

13,226. 

63. 

5214-1. 

25. 

1424. 

38. 

917-3. 

51. 

10,978. 

64. 

,  3279-3. 

26. 

1795. 

39. 

1959-2. 

52. 

10,908. 

65. 

,  8173-3. 

27. 

559. 

40. 

817-8. 

53. 

11,279-3. 

66. 

,  19,049-1. 

28. 

168. 

41. 

817-3. 

54. 

8247-2. 

29. 

1071. 

42. 

770-6. 

55. 

12,766-2. 

Lesson  51 

.    Page  160. 

1. 

164-34. 

10. 

109-11. 

19. 

117-:38. 

28. 

154-5. 

2. 

155-8. 

11. 

126-14. 

20. 

113-30. 

29. 

317-20. 

3. 

201-4. 

12. 

128-52. 

21. 

138-5. 

30. 

159-33. 

4. 

141-37. 

13. 

130-47. 

22. 

141-8. 

31. 

606-32. 

5. 

149-36. 

14. 

101-21. 

23. 

222-9. 

32. 

428-95. 

6. 

88-66. 

15. 

126-14. 

24. 

171-21. 

33. 

127-258. 

7. 

109-26. 

16. 

129-23. 

25. 

117-25. 

34. 

116-36. 

8. 

170-9. 

17. 

118-27. 

26. 

106-30. 

35. 

24-338. 

9. 

218-24. 

18. 

105-17. 

27. 

165-17. 

36. 

138-2. 

Lesson  52 

.    Page  161. 

1. 

139-389. 

15. 

112-618. 

29. 

1024^94. 

43. 

1298-187. 

2. 

278-54. 

16. 

127-336. 

30. 

761-173. 

44. 

1182-273. 

3. 

145-162. 

17. 

195-80. 

31. 

1363-134. 

45. 

4740-184. 

4. 

129-157. 

18. 

106-113. 

32. 

830-610. 

46. 

153-3330. 

5. 

109-196. 

19. 

219-207. 

33. 

682-69. 

47. 

406-1106. 

6. 

122-290. 

20. 

211-200. 

34. 

884-110. 

48. 

126-486. 

7. 

134-578. 

21. 

141-318. 

35. 

670-526. 

49. 

125-3932. 

8. 

79-164. 

22. 

108-825. 

36. 

724-80. 

50. 

140-3958. 

9. 

53-159. 

23. 

97-465. 

37. 

2315-55. 

51. 

108-4761. 

10. 

227-129. 

24. 

147-540. 

38. 

1347-189. 

52. 

127-464. 

11. 

237-210. 

25. 

1211-427. 

39. 

1009-210. 

53. 

83-2717. 

12. 

108-420. 

26. 

1160-105. 

40. 

1774-323. 

54. 

148-1854. 

13. 

121-135. 

27. 

807-12. 

41. 

654-1.52. 

14. 

103-622. 

28. 

223-805. 

42. 

2419-285. 

Lesson  53 

.    Page  162. 

1. 

$12. 

4. 

36  cts. 

8. 

$56. 

12. 

56  cts. 

2. 

8dys. 

5. 

$48. 

9. 

5. 

13. 

12  dys. 

3. 

§35. 

6. 

9. 

10. 

$14. 

14. 

6  lbs. 

7. 

55  cts. 

11. 

$20. 

211 


n2 

ANSWERS. 

Lesson  1. 

Page  163. 

1.  1.09. 

6. 

2.31. 

11.  22.1. 

16. 

33.8. 

2.  1.16. 

7. 

3.13. 

12.  47.3. 

17. 

0.131. 

3.  1.15. 

8. 

2.8. 

13.  2.34. 

18. 

1.64. 

4.  2.32. 

9. 

1.12. 

14.  0.653. 

19. 

1.21. 

5.  :].ll. 

10. 

22.4. 

15.  3.72. 

20. 

1.22. 

Lesson  2. 

Page  164. 

21. 

23.1. 

1.  430. 

11. 

50. 

21.  90. 

31. 

3.2. 

2.  305. 

12. 

60. 

22.  43. 

32. 

29. 

3.  272. 

13. 

60. 

23.  31. 

33. 

2.6. 

4.  290. 

14. 

90. 

24.  27. 

34. 

4.8. 

5.  230. 

15. 

1100. 

25.  3.1. 

35. 

1.1. 

6.  160. 

16. 

1100. 

26.  2.3. 

36. 

2.2. 

7.  130. 

17. 

1300. 

27.  16. 

37. 

22. 

8.  400. 

18. 

140. 

28.  3.6. 

38. 

310. 

9.  250. 

19. 

1600. 

29.  44. 

39. 

140. 

10.  402. 

20. 

180. 

30.  4.02. 

Lesson  3. 

Page  165. 

1.  10.03. 

9. 

0.017. 

17.  20,000. 

25. 

35,900. 

2.  3.1416. 

10. 

7.8. 

18.  500. 

26. 

24,163,000. 

3.  5.4. 

11. 

6.48. 

19.  1200. 

27. 

7.46. 

4.  8.17. 

12. 

2100. 

20.  2480. 

28. 

0.04. 

5.  115.1875. 

13. 

130. 

21.  20.3. 

29. 

40. 

6.  3692. 

14. 

5025. 

22.  8.302. 

30. 

400. 

7.  0.312. 

15. 

1040. 

23.  0.672. 

31. 

4900. 

8.  88. 

16. 

3,209,000. 
Lesson  4. 

24.  240.6. 
Page  166. 

32. 

0.04. 

1.  118. 

4. 

170. 

8.  256. 

12. 

5.5  ets. 

2.  37.50. 

5. 

29. 

9.  $125. 

13. 

28. 

3.  $2003. 

6. 

7. 

17. 
18. 

10.  109. 

11.  6.25. 

14. 

24. 

Lesson  5 

.    Page  167. 

1.  1.2109. 

3. 

24.2985 

6.  0.0029. 

9. 

0.0008. 

2.  3.iai3. 

4. 

140.6923. 

7.  0.0136. 

10. 

0.0001. 

5. 

0.0082. 

8.  0.0133. 

Lesson  6. 

Page  168. 

1.  5,798,758  tons. 

4. 

$693,048,702. 

7.  41.64  bu. 

2.   14.28  times. 

5. 

$69,786,800. 

8.  41  bu. 

3.  1,295,179  tons. 

6. 

165,831  acres. 

9.  14  bu. 

Lesson  8. 

Page  170. 

1.  13pts. 

3. 

57  pts. 

5.  65  pts. 

7.  : 

252  qts. 

2.  7  pts. 

4. 

36  gi. 

6.  90  pts. 

8. 

1512  pts. 

ANSWERS.  213 

9.  28  gals.  2  qts.  1  pt.      11.  45  gals.  2  qts.  1  pt.      13.   131  gals.  2  qts. 
10.  6  gals.  1  qt.  1  pt.         12.  55  gals.  1  qt.  14.  53  gals.  3  qts. 

1  pt.  3  gi. 
Lesson  9.    Page  171. 

1.  20  gals.  0  qt.  1  pt.      3.   103  gals.  1|  pts.         5.   10  gals.  3  qts.  1  pt. 

2.  48  gals.  1  qt.  4.  13  gals.  3  qts.  6.  9  gals.  3  qts.  I  pt. 

7.  21  gals.  1  qt.  1  pt. 
Lesson  10.    Page  172. 

1.  70  gals.  3  qts.  1  pt.     3.  31  qts.  5.  16  gals.  3  qts. 

2.  220  gals.  2  qts.  4.  21  gals.  1|  pts.  6.  16  gals.  1  qt.  1  pt. 

Lesson  11.    Page  173. 

1.  188  qts.  5.  21.  9.  411  bu.  1  pk.  2  qts. 

2.  63  bu.  1  pk.  4  qts.     6.  2  bu.  2  pks.  2  qts.    10.  2  bu.  3  qts. 

3.  69  bu.  1  pk.  7  qts.     7.  16  bu.  3  pks.  5  qts.   11.  3  bu.  1  pk.  7  qts. 

4.  3  bu.  2  pks.  6  qts.      8.  28  bu.  2  pks.  6  qts.    12.  13  bu.  2  pks.  6  qts. 


Lesson  12.  Page  174. 

1. 

2. 

8174  lbs. 
39  t.  596  lbs 

3.  18  t.       5.  5  t.  614  lbs.   7.  28  lbs.  6  oz. 
.  4.  1  t.  600  lbs.   6.  1  t.  500  lbs.   8.  81  cts. 

9.  §56.26. 
Lesson  13.  Page  175. 

1. 
2. 
3. 
4. 

1240. 
172  dwt. 
7  lbs.  4  oz. 
480. 

5.  0  oz.  15  dwt.      9.  53  oz.  6  dwt. 

6.  80  cts.         10.  165  oz.  18  dwt. 

7.  24.            11.  29oz.  18dwt.3grs. 

8.  109.          12.  4  oz.  0  dwt. 

Lesson  14.  Page  176. 

1. 
2. 
3. 

5012  min.     4.  5  dys.  13  hrs.  40  min.  7.  18  dys.  10  hrs. 
27,060  sec.    5.  1  yr.  2  dys.  1  hr.     8.  6  dys.  16  hrs.  18  min. 
14  dys.  4  hrs.   6.  1  wk.  1  dy.  9  hrs.        3  sec. 

9.  4  dys.  10  hrs.  42  min. 

Lesson  16.  Page  178. 

1. 
2. 
3. 
4. 
5. 
6. 
7. 

211  in. 
100  in. 
908  rds. 
6301  rds. 
3  mi. 
170  rds. 
2  mi.  80  rds. 

8.  11  mi.             15.  10  yds.  2  ft.  11  in. 

9.  48  yds.  11  in.        16.  18  yds.  6  in. 

10.  68  yds.  1  ft.  5  in.      17.  6  mi.  157  rds.  2^  ft. 

11.  30  mi.  89  rds.  4i  yds.   18.  8  mi.  187  rds.  31  ft. 

12.  39  mi.  275  rds.  14  ft.    19.  3  mi.  64  rds.  4ryds. 

13.  18  mi.  262  rds.  5  ft.    20.  9  mi.  32  rds.  4  yds. 

14.  1  mi.  272  rds.  15  ft.  11  in.  21.  171  yds.  1  ft.  3  in. 

22.  283  rds.  5  yds.  2  ft. 

Lesson  17.  Page  179. 

1. 

2. 

60  ft. 

84  ft. 

3.  68  ft.      5.  $120.            7.  3.5  in. 

4.  90  ft.      6.  66  in.:  88  in.;  22  ft.   8.  10.5  in. 

214  ANSWERS. 

Lesson  18.  Page  180. 

1.  4570  sq.  ft.   4.  312  sq.  ft.  68  sq.  in.  7.  13  A.  75  sq.  rds. 

2.  5  A.       5.  14  A,  8.  9  sq.  yds.  7  sq.  ft.  20  sq.  in. 

3.  570  sq.  rds.   6.  533  A.  36  sq.  rds.    9.  19  A.  20  sq.  rds. 

Lesson  19.  Page  181. 

1.  40  sq.  in.   5.  90  sq.  in.   9.  16  sq.ft.  13.  4  sq.  yds. 

2.  54  sq.  in.   6.  64  sq.  in.  10.  420  sq.  ft.  14.  986  sq,  yds. 

3.  56  sq.  in.   7.6  sq.  ft.   11.  270  sq.  in.  15.  80  sq.  rds. 

4.  110  sq.  in.  8.  8  sq.  ft.   12.  36  sq.  ft.  16.  594  sq.  ft. 

Lesson  20.  Page  182. 

1.  860  sq.  ft.     3.  72  sq.  yds.   5.  16  sq.  yds.   7.  112  sq.  in. 

2.  30  sq.  yds.    4.  10  A.       6.  32  sq.  yds.   8.  122  sq.  in. 

10.  314  sq.  in.  ;  805  sq.  in. ;  1257  sq.  in.    9.  54  sq.  ft. 

11.  805  sq.  in. ;  1018  sq.  in. 

12.  380  sq.  in. ;  616  sq.  in. 

13.  707  sq.  in. ;  1257  sq.  in.  ;  1521  sq.  in. ;  1663  sq.  in. 

14.  1964  sq.  in. 

Lesson  21.    Page  183. 
1.  5  strips.  2.  10  strips.  3.  35  yds. ;  ^  yd. 

Lesson  22.    Page  184. 
1.  8.  2.  38.00.  3.  34.50.  4.  10.  5.  9. 


Lesson  23, 

,    Page  185. 

1. 

372  cu.  ft. 

4.   175  cu, 

.  yds.  7  cu 

..ft 

.    7.  lOcds. 

2. 

22 

cu. 

yds. 

6  cu.  ft. 

5.  1  cu.  yd.  16  cu. 

ft. 

8.  15  cds.  96  cd.  ft. 

3. 

23 

cu. 

yds. 

25.  cu.  ft. 

6.  64 cu.; 

j^ds.  25cu 

.  ft 

.     9.  4cu. 
10.   $9. 

yds.  20  cu.  ft. 

Lesson  24. 

Page  186. 

1. 

96 

cu. 

in. 

4.  84  cu. 

in. 

7. 

30  cu.  ft. 

2. 

48 

cu. 

in. 

5.  320  cu 

.  in. 

8, 

462  cu.  yds. 

3. 

64 

cu. 

in. 

6.  27  cu.  1 

ft.  or  1  cu, 

yd 

9. 

264  cu.  yds. 

Lesson  30 

.    Page  192. 

1. 

3. 

5. 

7. 

9.  3f 

13.  171, 

17.  6|. 

21.  3,V 

2. 

6. 

6. 

9. 

10.  6|. 

14.  3|. 

18.  31. 

22.  3-fV 

3. 

2. 

7. 

3i 

11.  61. 

15.  31 

19,  4|. 

23.  2,V. 

4. 

6. 

8. 

9f. 

12.  5tV 

16.  4f. 

20.  SI. 

24.  5H. 

1. 

f. 

5. 

f- 

9.  f. 

13.  I 

17.  h 

21.  f. 

2. 

I 

6. 

h 

10.  f. 

14.  f. 

18.   f. 

22.  f. 

3. 

i- 

7. 

h 

11.  f. 

15.  i- 

19.  f. 

23.  4. 

4. 

h 

8. 

I 

12.  f 

16.  I. 

20.  f. 

24.  i. 

ANSWERS. 


215 


1.  f. 

2.  f 

3.  A. 

1.  5. 

2.  7. 

3.  6?. 


4.  f 

5.  A. 

6.  ^. 


4.  10. 

5.  6^. 

6.  15i 


Lesson  31.    Page  193. 

7.  t-           10.  tV         13.  i  16.  i. 

8.  T^j.         11.  ^.         14.  i.  17.  f 

9.  ^,.         12.  /r-         15.  f  18.  :>f. 

Lesson  32.    Page  194. 

7.  91.       10.  8^.        13.   16|.      16.  12. 

8.  9|.       11.   14.         14.  12|.      17.  18. 

9.  13.       12.   16i.       15.   11.        18.  24. 


19.  5|. 

20.  105, 

21.  16. 


15.     3.  20.     5.  25.    7.  22.      9.  70.    11.  150^.    13.   17.     15.  22. 
14.    4.  21.    6.  30.    8.  24.    10.  46.    12.  184|.    14.  27^. 


2. 


Lesson  33.    Page  195. 


7.  2^. 

8.  15. 

10.  1^. 

11.  H. 

12.  f 


13.  i. 

14.  f 

15.  1|. 

16.  H. 

17.  |. 

18.  |. 

Lesson  34.    Page  196. 


19.  i 

20.  1^. 

21.  4. 

22.  1|. 

23.  3. 

24.  3. 


25.  II 

26.  2. 

27.  i 

28.  f. 

29.  2. 

30.  1. 


31.  5. 

32.  3. 

33.  1^. 

34.  2. 

35.  \. 

36.  5. 


4         9        10 
TJ'  TJ'  T2' 

TJ'  T2'  T2- 

TJ»  rV  tI- 

h  h  f- 

f- 

3 

27  in. 
10  oz. 
1000  lbs. 
24  cu.  ft. 


5  6       10       7 

.  TJi  T8'  T5- 

6.  hh  /t.  /f 

7.  1^5,  il,  t\. 
8. 


9.    T5>  T^7»  T5- 

10.  it,  ft,  ||. 

11-    H,   I?,  ^. 
10      21      11       8 

±Al.        OS.      IfS,      TfTT. 


13. 
14. 
15. 


Ih 


ii»  T2'  tV 

H,  'rh  H' 


2T'  2T- 

Lesson  37.    Page  199. 


7.  H- 

9.  7^3^. 
10.  34. 


11.  Iff. 

12.  7|. 

13.  0.06. 

14.  0.15. 

15.  0.025. 


16.  0.04. 

17.  0.135. 

18.  0.032. 

19.  0.004. 

20.  17.875. 


Lesson  38.    Page  200. 

6.  112cd.  ft.   11.  27qrs.;29  15.  36  cts. 

7.  li^  pts.  qrs.  16.  21  cts. 

8.  16  hrs.        12.  9  halves.     17.  7  mi. 

9.  45min.       13.   11.  18.  7|  mi. 


120  sq.  rds.     10.  8  qrs. 


14.  2  gals.         19.  lOimi. 


Lesson  39.    Page  201. 


$0.90 

$0.81 
$1.63 
$1.78 
$5.21 


6.  $1.98. 

7.  $6.00. 

8.  $27.00. 

9.  $31.50. 
10.  $0.95. 


11.  $1.04. 

12.  $0.84. 

13.  $3.05. 

14.  $2.02. 

15.  $6.21. 


16.  $29.48. 

17.  $13.44. 

18.  $19.25. 

19.  $6.16. 

20.  $2.24. 


21.  5.375. 

22.  7.075. 

23.  1.9375. 

24.  5.0625. 


20.  I  yd. 

21.  $5i. 

22.  $5\. 

23.  $1.80. 


21.  $7.16. 

22.  $15.60. 

23.  $1.40. 

24.  $506.25. 

25.  $884.25. 


216  ANSWERS. 

Lesson  42.    Page  204. 
1.  $9.46.  2.  $21.45.  3.  $24.88.  4.  $18.24. 

Lesson  44.    Page  206. 

1.  10.5.        3.  80  men.  5.  156  dys.         7.  608  oz.  9.  1530  ft. 

2.75.  4.  36  sheep.         6.  $280.  8.  1012  lbs.       10.  206  mi. 

1.  33i%.      3.  3000/0.  5.  20%.  7.  75  o/,.  9.  89^%. 

2.  2^%.        4.  4000%.  6.  20%.  8.  12/^%.  10.  82f  %. 

Lesson  45.    Page  207. 

1.  $18.31.  3.  $7.82.  6.  $106,265.  9.  $1530. 

2.  $41.88.  4.  $103.14.  7.  $316.99.  10.  $76.76. 

5.  $131.40.  8.  $1020. 

Lesson  46.    Page  208. 

1.  $18.  4.  $82.29.       7.  $0.11.       10.  $134.02.         13.  $106,805. 

2.  $24.75.      5.  $19.88.       8.  $1.76.       11.  $1266.67.       14.  $26.52. 

3.  $124.         6.  $31.25.       9.  $6.61.       12.  $41.09.  15.  $48.53. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


6N0VM8JI8 

DUE 


LD  21-100m-9,'47(A5702sl6)476 


r  b    I / 44 / 


UNIVERSITY  OF  CALIFORNIA  UBRARY 


